Calculus and mathematical analysis Books
Single Variable Essential Calculus
Book SynopsisThis book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? SINGLE VARIABLE ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 550 pages--two-fifths the size of Stewart's other calculus texts (CALCULUS, Seventh Edition and CALCULUS: EARLY TRANSCENDENTALS, Seventh Edition) and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as promineTable of Contents1. FUNCTIONS AND LIMITS. Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity. 2. DERIVATIVES. Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials. 3. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives. 4. INTEGRALS. Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule. 5. INVERSE FUNCTIONS. Inverse Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule. 6. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals. 7. APPLICATIONS OF INTEGRATION. Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations. 8. SERIES. Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials. 9. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Appendix A: Trigonometry Appendix B: Proofs Appendix C: Sigma Notation
£217.00
Bloomsbury Publishing PLC How to Analyze Data Pocket Study Skills
Book SynopsisCatrin Radcliffe is a tutor of mathematics and statistics at Oxford Brookes University, UK.Table of ContentsIntroduction PART 1: GETTING STARTED 1. What does your assignment ask you to do? 2. How will you do it? 3. Defining your research question 4. Tips for designing your questionnaire 5. How to enter your data into a spreadsheet PART 2: UNDERSTANDING AND DESCRIBING YOUR DATA 6. What type of data do you have? 7. Descriptive statistics 8. What plot should you use? PART 3: HOW DO STATISTICAL TESTS WORK? 9. What is a statistical hypothesis? 10. Using probability distributions in statistical tests 11. Statistics, "errors" and interpretation PART 4: WHAT STATISTICAL TEST DO YOU NEED? 12. The statistics signpost 13. Statistical flowcharts 14. Case studies PART 5: THE STATISTICAL PROCESS 15. You the researcher 16. You the interpreter Symbols explained Useful resources References Index.
£10.13
Taylor & Francis Ltd An Illustrative Introduction to Modern Analysis
Book SynopsisAimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis.The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.Table of ContentsSets, mappings, countability and choice. Metric spaces and normed spaces. Completeness and applications. Topological spaces and continuity. Compactness and sequential compactness. The Lebesgue measure on the Euclidean space. Measure theory on general spaces. The Lebesgue integration theory. The class of Lebesgue functional spaces. Inner product spaces and Hilbert spaces. Linear operators on normed spaces. Weak topologies on Banach spaces. Weak* topologies and compactness. Functional properties of the Lebesgue spaces. Solutions to the exercises.
£99.75
Pearson Education Limited College Algebra
Book SynopsisTable of ContentsP. Prerequisites: Fundamental Concepts of Algebra P.1 Algebraic Expressions, Mathematical Models, and Real Numbers P.2 Exponents and Scientific Notation P.3 Radicals and Rational Exponents P.4 Polynomials Mid-Chapter Check Point P.5 Factoring Polynomials P.6 Rational Expressions SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER P TEST 1. Equations and Inequalities 1.1 Graphs and Graphing Utilities 1.2 Linear Equations and Rational Equations 1.3 Models and Applications 1.4 Complex Numbers 1.5 Quadratic Equations Mid-Chapter Check Point 1.6 Other Types of Equations 1.7 Linear Inequalities and Absolute Value Inequalities SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 1 TEST 2. Functions and Graphs 2.1 Basics of Functions and Their Graphs 2.2 More on Functions and Their Graphs 2.3 Linear Functions and Slope 2.4 More on Slope Mid-Chapter Check Point 2.5 Transformations of Functions 2.6 Combinations of Functions; Composite Functions 2.7 Inverse Functions 2.8 Distance and Midpoint Formulas; Circles SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 2 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2) 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Polynomial Functions and Their Graphs 3.3 Dividing Polynomials; Remainder and Factor Theorems 3.4 Zeros of Polynomial Functions Mid-Chapter Check Point 3.5 Rational Functions and Their Graphs 3.6 Polynomial and Rational Inequalities 3.7 Modeling Using Variation SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 3 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3) 410 4. Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Properties of Logarithms Mid-Chapter Check Point 4.4 Exponential and Logarithmic Equations 4.5 Exponential Growth and Decay; Modeling Data SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 4 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4) 5. Systems of Equations and Inequalities 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations in Three Variables 5.3 Partial Fractions 5.4 Systems of Nonlinear Equations in Two Variables Mid-Chapter Check Point 5.5 Systems of Inequalities 5.6 Linear Programming SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 5 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5) 6. Matrices and Determinants 6.1 Matrix Solutions to Linear Systems 6.2 Inconsistent and Dependent Systems and Their Applications 6.3 Matrix Operations and Their Applications Mid-Chapter Check Point 6.4 Multiplicative Inverses of Matrices and Matrix Equations 6.5 Determinants and Cramer's Rule SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 6 TEST CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6) 7. Conic Sections 7.1 The Ellipse 7.2 The Hyperbola Mid-Chapter Check Point 7.3 The Parabola SUMMARY, REVIEW, AND TEST REVIEW EXERCISES CHAPTER 7 TEST
£64.99
Pearson Education Second Course in Statistics A Regression Analysis
Book SynopsisTable of Contents1. A Review of Basic Concepts (Optional) 1.1 Statistics and Data 1.2 Populations, Samples, and Random Sampling 1.3 Describing Qualitative Data 1.4 Describing Quantitative Data Graphically 1.5 Describing Quantitative Data Numerically 1.6 The Normal Probability Distribution 1.7 Sampling Distributions and the Central Limit Theorem 1.8 Estimating a Population Mean 1.9 Testing a Hypothesis About a Population Mean 1.10 Inferences About the Difference Between Two Population Means 1.11 Comparing Two Population Variances 2. Introduction to Regression Analysis 2.1 Modeling a Response 2.2 Overview of Regression Analysis 2.3 Regression Applications 2.4 Collecting the Data for Regression 3. Simple Linear Regression 3.1 Introduction 3.2 The Straight-Line Probabilistic Model 3.3 Fitting the Model: The Method of Least Squares 3.4 Model Assumptions 3.5 An Estimator of s2 3.6 Assessing the Utility of the Model: Making Inferences About the Slope ß1 3.7 The Coefficient of Correlation 3.8 The Coefficient of Determination 3.9 Using the Model for Estimation and Prediction 3.10 A Complete Example 3.11 Regression Through the Origin (Optional) Case Study 1: Legal Advertising--Does It Pay? 4. Multiple Regression Models 4.1 General Form of a Multiple Regression Model 4.2 Model Assumptions 4.3 A First-Order Model with Quantitative Predictors 4.4 Fitting the Model: The Method of Least Squares 4.5 Estimation of s2, the Variance of e 4.6 Testing the Utility of a Model: The Analysis of Variance F-Test 4.7 Inferences About the Individual ß Parameters 4.8 Multiple Coefficients of Determination: R2 and R2adj 4.9 Using the Model for Estimation and Prediction 4.10 An Interaction Model with Quantitative Predictors 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor 4.12 More Complex Multiple Regression Models (Optional) 4.13 A Test for Comparing Nested Models 4.14 A Complete Example Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods 5. Principles of Model Building 5.1 Introduction: Why Model Building is Important 5.2 The Two Types of Independent Variables: Quantitative and Qualitative 5.3 Models with a Single Quantitative Independent Variable 5.4 First-Order Models with Two or More Quantitative Independent Variables 5.5 Second-Order Models with Two or More Quantitative Independent Variables 5.6 Coding Quantitative Independent Variables (Optional) 5.7 Models with One Qualitative Independent Variable 5.8 Models with Two Qualitative Independent Variables 5.9 Models with Three or More Qualitative Independent Variables 5.10 Models with Both Quantitative and Qualitative Independent Variables 5.11 External Model Validation 6. Variable Screening Methods 6.1 Introduction: Why Use a Variable-Screening Method? 6.2 Stepwise Regression 6.3 All-Possible-Regressions Selection Procedure 6.4 Caveats Case Study 3: Deregulation of the Intrastate Trucking Industry 7. Some Regression Pitfalls 7.1 Introduction 7.2 Observational Data Versus Designed Experiments 7.3 Parameter Estimability and Interpretation 7.4 Multicollinearity 7.5 Extrapolation: Predicting Outside the Experimental Region 7.6 Variable Transformations 8. Residual Analysis 8.1 Introduction 8.2 Plotting Residuals 8.3 Detecting Lack of Fit 8.4 Detecting Unequal Variances 8.5 Checking the Normality Assumption 8.6 Detecting Out
£69.18
Pearson Education Calculus And Its Applications Global Edition
Book SynopsisMarvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999.Table of ContentsR. Functions, Graphs, and Models R.1 Graphs and Equations R.2 Functions and Models R.3 Finding Domain and Range R.4 Slope and Linear Functions R.5 Nonlinear Functions and Models R.6 Mathematical Modeling and Curve Fitting Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application Average Price of a Movie Ticket 1. Differentiation 1.1 Limits: A Numerical and Graphical Approach 1.2 Algebraic Limits and Continuity 1.3 Average Rates of Change 1.4 Differentiation Using Limits of Difference Quotients 1.5 The Power and Sum—Difference Rules 1.6 The Product and Quotient Rules 1.7 The Chain Rule 1.8 Higher-Order Derivatives Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Path of a Baseball: The Tale of the Tape 2. Applications of Differentiation 2.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 2.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 2.3 Graph Sketching: Asymptotes and Rational Functions 2.4 Using Derivatives to Find Absolute Maximum and Minimum Values 2.5 Maximum—Minimum Problems; Business, Economics, and General Applications 2.6 Marginals and Differentials 2.7 Elasticity of Demand 2.8 Implicit Differentiation and Related Rates Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Maximum Sustainable Harvest 3. Exponential and Logarithmic Functions 3.1 Exponential Functions 3.2 Logarithmic Functions 3.3 Applications: Uninhibited and Limited Growth Models 3.4 Applications: Decay 3.5 The Derivatives of ax and loga x 3.6 A Business Application: Amortization Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–The Business of Motion Picture Revenue and DVD Release 4. Integration 4.1 Antidifferentiation 4.2 Antiderivatives as Areas 4.3 Area and Definite Integrals 4.4 Properties of Definite Integrals 4.5 Integration Techniques: Substitution 4.6 Integration Techniques: Integration by Parts 4.7 Integration Techniques: Tables Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Business: Distribution of Wealth 5. Applications of Integration 5.1 Consumer Surplus and Producer Surplus 5.2 Integrating Growth and Decay Models 5.3 Improper Integrals 5.4 Probability 5.5 Probability: Expected Value; The Normal Distribution 5.6 Volume 5.7 Differential Equations Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Curve Fitting and Volumes of Containers 6. Functions of Several Variables 6.1 Functions of Several Variables 6.2 Partial Derivatives 6.3 Maximum—Minimum Problems 6.4 An Application: The Least-Squares Technique 6.5 Constrained Optimization 6.6 Double Integrals Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application–Minimizing Employees’ Travel Time in a Building Cumulative Revi
£64.99
Pearson Education Limited Calculus with Applications Global Edition
Book SynopsisTable of Contents R. Algebra Reference R-1 Polynomials R-2 Factoring R-3 Rational Expressions R-4 Equations R-5 Inequalities R-6 Exponents R-7 Radicals 1. Linear Functions 2. Nonlinear Functions 3. The Derivative 4. Calculating the Derivative 5. Graphs and the Derivative 6. Applications of the Derivative 7. Integration 8. Further Techniques and Applications of Integration 9. Multivariable Calculus 10. Differential Equations 11. Probability and Calculus 12. Sequences and Series 13. The Trigonometric Functions Tables Answers to Selected Exercises Photo Acknowledgements Index
£76.94
Pearson Education Limited Calculus with Applications Global Edition MyLab
Book SynopsisThis package includes MyMathLab. For freshman/sophomore, 2-semester (2-3 quarter) courses covering applied calculus for students in business, economics, social sciences, or life sciences. Calculus with Applications, Eleventh Edition by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to help them learn the material, such as Warm-Up Exercises and added help text within examples. This package includes MyMathLab, an online homework, tutorial, and assessment program designed to work with this text to personalize learning and improve results. With a wide range of inte
£86.85
Pearson Education Calculus for Business Economics Life Sciences and
Book Synopsis
£84.86
Pearson Education University Calculus Early Transcendentals Global
Book SynopsisTable of Contents1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Software 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 2. Limits and Continuity 2.1 Rates of Change and Tangent Lines to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity; Asymptotes of Graphs Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 3. Derivatives 3.1 Tangent Lines and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Differentiation Rules 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 4. Applications of Derivatives 4.1 Extreme Values of Functions on Closed Intervals 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L’Hôpital’s Rule 4.6 Applied Optimization 4.7 Newton’s Method 4.8 Antiderivatives Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 5. Integrals 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Method 5.6 Definite Integral Substitutions and the Area Between Curves Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 7. Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions Questions to Guide Your Review Practice Exercises Additional and Advanced Exercises 8. Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions
£75.04
Pearson Education Thomas Calculus SI Units MyLab Mathematics with
Book Synopsis
£78.84
Pearson Education Thomas Calculus Early Transcendentals SI Units
Book SynopsisJoel Hass received his PhD from the University of California - Berkeley. He is currently a professor of mathematics at the University of California - Davis. He has coauthored widely used calculus texts as well as calculus study guides. He is currently on the editorial board of several publications, including the Notices of the American Mathematical Society. He has been a member of the Institute for Advanced Study at Princeton University and of the Mathematical Sciences Research Institute, and he was a Sloan Research Fellow. Hass's current areas of research include the geometry of proteins, three dimensional manifolds, applied math, and computational complexity. In his free time, Hass enjoys kayaking. Christopher Heil received his PhD from the University of Maryland. He is currently a professor of mathematics at the Georgia Institute of Technology. He is the author of a graduate text on analysis and a number of highly cited research survey art
£80.24
Cengage Learning, Inc Calculus An Applied Approach Brief
Book SynopsisTable of Contents1. FUNCTIONS, GRAPHS, AND LIMITS. The Cartesian Plane and the Distance Formula. Graphs of Equations. Lines in the Plane and Slope. Functions. Limits. Continuity. 2. DIFFERENTIATION. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule. Higher-Order Derivatives. Implicit Differentiation. Related Rates. 3. APPLICATIONS OF THE DERIVATIVE. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test. Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. 5. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and the General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum. 6. TECHNIQUES OF INTEGRATION. Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals. 7. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals.
£338.36
Cambridge University Press Mathematical Aspects of Deep Learning
Book SynopsisIn recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves both as a starting point for researchers and graduate students in computer science, mathematics, and statistics trying to get into the field and as an invaluable reference for future research.Table of Contents1. The modern mathematics of deep learning Julius Berner, Philipp Grohs, Gitta Kutyniok and Philipp Petersen; 2. Generalization in deep learning Kenji Kawaguchi, Leslie Pack Kaelbling, and Yoshua Bengio; 3. Expressivity of deep neural networks Ingo Gühring, Mones Raslan and Gitta Kutyniok; 4. Optimization landscape of neural networks René Vidal, Zhihui Zhu and Benjamin D. Haeffele; 5. Explaining the decisions of convolutional and recurrent neural networks Wojciech Samek, Leila Arras, Ahmed Osman, Grégoire Montavon and Klaus-Robert Müller; 6. Stochastic feedforward neural networks: universal approximation Thomas Merkh and Guido Montúfar; 7. Deep learning as sparsity enforcing algorithms A. Aberdam and J. Sulam; 8. The scattering transform Joan Bruna; 9. Deep generative models and inverse problems Alexandros G. Dimakis; 10. A dynamical systems and optimal control approach to deep learning Weinan E, Jiequn Han and Qianxiao Li; 11. Bridging many-body quantum physics and deep learning via tensor networks Yoav Levine, Or Sharir, Nadav Cohen and Amnon Shashua.
£66.49
Cambridge University Press Elliptic and Hyperelliptic Integrals and Allied Theory
Originally published in 1938, this book focuses on the area of elliptic and hyperelliptic integrals and allied theory. The text was a posthumous publication by William Westropp Roberts (18501935), who held the position of Vice-Provost at Trinity College, Dublin from 1927 until shortly before his death.
£36.09
Cambridge University Press Analytic Semigroups and Semilinear Initial
Book SynopsisA careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.Table of Contents1. Introduction and main results; 2. Preliminaries from functional analysis; 3. Theory of analytic semigroups; 4. Sobolev imbedding theorems; 5. Lp theory of pseudo-differential operators; 6. Lp approach to elliptic boundary value problems; 7. Proof of theorem 1.1; 8. Proof of theorem 1.2; 9. Proof of theorems 1.3 and 1.4; Appendix A. The Laplace Transform; Appendix B. The Maximum Principle; Appendix C. Vector bundles; References; Index.
£58.25
Cengage Learning, Inc Precalculus
Table of Contents1. FUNCTIONS AND THEIR GRAPHS. Rectangular Coordinates. Graphs of Equations. Linear Equations in Two Variables. Functions. Analyzing Graphs of Functions. A Library of Parent Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros of Polynomial Functions. Rational Functions. Nonlinear Inequalities. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 1-3. Proofs in Mathematics. P.S. Problem Solving. 4. TRIGONOMETRY. Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 5. ANALYTIC TRIGONOMETRY. Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 6. ADDITIONAL TOPICS IN TRIGONOMETRY. Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. The Complex Plane. Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 4-6. Proofs in Mathematics. P.S. Problem Solving. 7. SYSTEMS OF EQUATIONS AND INEQUALITIES. Linear and Nonlinear Systems of Equations. Two-Variable Linear Systems. Multivariable Linear Systems. Partial Fractions. Systems of Inequalities. Linear Programming. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 8. MATRICES AND DETERMINANTS. Matrices and Systems of Equations. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. 9. SEQUENCES, SERIES, AND PROBABILITY. Sequences and Series. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Mathematical Induction. The Binomial Theorem. Counting Principles. Probability. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test for Chapters 7-9. Proofs in Mathematics. P.S. Problem Solving. 10. TOPICS IN ANALYTIC GEOMETRY. Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas. Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs of Polar Equations. Polar Equations of Conics. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem Solving. APPENDIX A. Review of Fundamental Concepts of Algebra. A.1 Real Numbers and Their Properties. A.2 Exponents and Radicals. A.3 Polynomials and Factoring. A.4 Rational Expressions. A.5 Solving Equations. A.6 Linear Inequalities in One Variable. A.7 Errors and the Algebra of Calculus. APPENDIX B. Concepts in Statistics (Web). B.1 Representing Data. B.2 Analyzing Data. B.3 Modeling Data.
£202.35
Cengage Learning, Inc Calculus
Book SynopsisTable of ContentsP. PREPARATION FOR CALCULUS. Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Review of Trigonometric Functions. Review Exercises. P.S. Problem Solving. 1. LIMITS AND THEIR PROPERTIES. A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits. Section Project: Graphs and Limits of Trigonometric Functions. Review Exercises. P.S. Problem Solving. 2. DIFFERENTIATION. The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Section Project: Optical Illusions. Related Rates. Review Exercises. P.S. Problem Solving. 3. APPLICATIONS OF DIFFERENTIATION. Extrema on an Interval. Rolle"s Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Section Project: Even Fourth-Degree Polynomials. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Minimum Time. Newton"s Method. Differentials. Review Exercises. P.S. Problem Solving. 4. INTEGRATION. Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Review Exercises. P.S. Problem Solving. 5. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS. The Natural Logarithmic Function: Differentiation. The Natural Logarithmic Function: Integration. Inverse Functions. Exponential Functions: Differentiation and Integration. Bases Other than e and Applications. Section Project: Using Graphing Utilities to Estimate Slope. Indeterminate Forms and L'Hopital's Rule. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: Mercator Map. Review Exercises. P.S. Problem Solving. 6. DIFFERENTIAL EQUATIONS. Slope Fields and Euler"s Method. Growth and Decay. Separation of Variables and the Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. Review Exercises. P.S. Problem Solving. 7. APPLICATIONS OF INTEGRATION. Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method. Section Project: Saturn. Arc Length and Surfaces of Revolution. Work. Section Project: Pyramid of Khufu. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. Review Exercises. P.S. Problem Solving. 8. INTEGRATION TECHNIQUES AND IMPROPER INTEGRALS. Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: The Wallis Product. Trigonometric Substitution. Partial Fractions. Numerical Integration. Integration by Tables and Other Integration Techniques. Improper Integrals. Review Exercises. P.S. Problem Solving. 9. INFINITE SERIES. Sequences. Series and Convergence. Section Project: Cantor"s Disappearing Table. The Integral Test and p-Series. Section Project: The Harmonic Series. Comparisons of Series. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series. Review Exercises. P.S. Problem Solving. 10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES. Conics and Calculus. Plane Curves and Parametric Equations. Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs. Section Project: Cassini Oval. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler"s Laws. Review Exercises. P.S. Problem Solving. 11. VECTORS AND THE GEOMETRY OF SPACE. Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving. 12. VECTOR-VALUED FUNCTIONS. Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving. 13. FUNCTIONS OF SEVERAL VARIABLES. Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving. 14. MULTIPLE INTEGRATION. Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Surface Area in Polar Coordinates. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving. 15. VECTOR ANALYSIS. Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green"s Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes" Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving. 16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE. Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving. APPENDIX. A. Proofs of Selected Theorems. B. Integration Tables. C. Precalculus Review (Web). C.1. Real Numbers and the Real Number Line. C.2. The Cartesian Plane. D. Rotation and the General Second-Degree Equation (Web). E. Complex Numbers (Web). F. Business and Economic Applications (Web). G. Fitting Models to Data (Web).
£218.19
Precalculus
Book SynopsisYear after year, PRECALCULUS: FUNCTIONS AND GRAPHS leads the way in helping students like you succeed in their Precalculus courses. Its clear explanations and examples and exercises featuring a variety of real-life applications make the content understandable and relatable. This 13th edition of Swokowski and Cole's bestselling text is consistently praised for being at just the right level for Precalculus students. Perhaps most important, this book effectively prepares readers for further courses in mathematics.Table of Contents1. TOPICS FROM ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities. 2. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater Than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 5. TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of the Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 6. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Additions and Subtraction of Formulas. Multiple-Angle Formulas. Product-To-Sum and Sum-To-Product Formulas. The Inverse Trigonometric Functions. 7. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre���s Theorem and nth Roots of Complex Numbers. 8. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 9. SEQUENCES, SERIES, AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 10. TOPICS FROM ANALYTICAL GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. 11. LIMITS OF FUNCTIONS. Introductions to Limits. Definition of a Limit. Techniques for Finding Limits. Limits Involving Infinity. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle. Appendix V: Theorems on Limits.
£260.77
Cengage Learning Calculus of a Single Variable
£247.50
Cengage Learning, Inc Physics for Scientists and Engineers
Book SynopsisTable of ContentsPART I: MECHANICS. 1. Physics and Measurement. 2. Motion in One Dimension. 3. Vectors. 4. Motion in Two Dimensions. 5. The Laws of Motion. 6. Circular Motion and Other Applications of Newton's Laws. 7. Energy of a System. 8. Conservation of Energy. 9. Linear Momentum and Collisions. 10. Rotation of a Rigid Object About a Fixed Axis. 11. Angular Momentum. 12. Static Equilibrium and Elasticity. 13. Universal Gravitation. 14. Fluid Mechanics. PART II: OSCILLATIONS AND MECHANICAL WAVES. 15. Oscillatory Motion. 16. Wave Motion. 17. Superposition and Standing Waves. PART III: THERMODYNAMICS. 18. Temperature. 19. The First Law of Thermodynamics. 20. The Kinetic Theory of Gases. 21. Heat Engines, Entropy, and the Second Law of Thermodynamics. Part IV: ELECTRICITY AND MAGNETISM. 22. Electric Fields. 23. Continuous Charge Distributions and Gauss's Law. 24. Electric Potential. 25. Capacitance and Dielectrics. 26. Current and Resistance. 27. Direct-Current Circuits. 28. Magnetic Fields. 29. Sources of the Magnetic Field. 30. Faraday's Law. 31. Inductance. 32. Alternating-Current Circuits. 33. Electromagnetic Waves. PART V: LIGHT AND OPTICS. 34. The Nature of Light and the Principles of Ray Optics 35. Image Formation. 36. Wave Optics. 37. Diffraction Patterns and Polarization. PART VI: MODERN PHYSICS. 38. Relativity. APPENDICES. A. Tables. B. Mathematics Review. C. Periodic Table of the Elements. D. SI Units. Answers to Quick Quizzes and Odd-Numbered Problems. Index.
£71.24
Johns Hopkins University Press Least Squares Data Fitting with Applications
Book SynopsisSuitable for anyone working with problems of linear and nonlinear least squares fitting, this book includes an overview of computational methods together with their properties and advantages. It also includes topics from statistical regression analysis that help readers to understand and evaluate the computed solutions.Trade ReviewLeast Square Data fitting with Applications is a book that will be of great practical use to anyone whose work involves the analysis of data and its modeling. It offers a great deal of information that can be a s valuable in the lecture theater as in the lab or office. Mathematics TodayTable of ContentsPrefaceSymbols and AcronymsChapter 1. The Linear Data Fitting Problem1.1. Parameter estimation, data approximation1.2. Formulation of the data fitting problem1.3. Maximum likelihood estimation1.4. The residuals and their properties1.5. Robust regressionChapter 2. The Linear Least Squares Problem2.1. Linear least squares problem formulation2.2. The QR factorization and its role2.3. Permuted QR factorizationChapter 3. Analysis of Least Squares Problems3.1. The pseudoinverse3.2. The singular value decomposition3.3. Generalized singular value decomposition3.4. Condition number and column scaling3.5. Perturbation analysisChapter 4. Direct Methods for Full-Rank Problems4.1. Normal equations4.2. LU factorization4.3. QR factorization4.4. Modifying least squares problems4.5. Iterative refinement4.6. Stability and condition number estimation4.7. Comparison of the methodsChapter 5. Direct Methods for Rank-Deficient Problems5.1. Numerical rank5.2. Peters-Wilkinson LU factorization5.3. QR factorization with column permutations5.4. UTV and VSV decompositions5.5. Bidiagonalization5.6. SVD computationsChapter 6. Methods for Large-Scale Problems6.1. Iterative versus direct methods6.2. Classical stationary methods6.3. Non-stationary methods, Krylov methods6.4. Practicalities: preconditioning and stopping criteria6.5. Block methodsChapter 7. Additional Topics in Least Squares7.1. Constrained linear least squares problems7.2. Missing data problems7.3. Total least squares (TLS)7.4. Convex optimization7.5. Compressed sensingChapter 8. Nonlinear Least Squares Problems8.1. Introduction8.2. Unconstrained problems8.3. Optimality conditions for constrained problems8.4. Separable nonlinear least squares problems8.5. Multiobjective optimizationChapter 9. Algorithms for Solving Nonlinear LSQ Problems9.1. Newton's method9.2. The Gauss-Newton method9.3. The Levenberg-Marquardt method9.4. Additional considerations and software9.5. Iteratively reweighted LSQ algorithms for robust data fitting problems9.6. Variable projection algorithm9.7. Block methods for large-scale problemsChapter 10. Ill-Conditioned Problems10.1. Characterization10.2. Regularization methods10.3. Parameter selection techniques10.4. Extensions of Tikhonov regularization10.5. Ill-conditioned NLLSQ problemsChapter 11. Linear Least Squares Applications11.1. Splines in approximation11.2. Global temperatures data fitting11.3. Geological surface modelingChapter 12. Nonlinear Least Squares Applications12.1. Neural networks training12.2. Response surfaces, surrogates or proxies12.3. Optimal design of a supersonic aircraft12.4. NMR spectroscopy12.5. Piezoelectric crystal identification12.6. Travel time inversion of seismic dataAppendix A: Sensitivity AnalysisA.1. Floating-point arithmeticA.2. Stability, conditioning and accuracyAppendix B: Linear Algebra BackgroundB.1. NormsB.2. Condition numberB.3. OrthogonalityB.4. Some additional matrix propertiesAppendix C: Advanced Calculus BackgroundC.1. Convergence ratesC.2. Multivariable calculusAppendix D: StatisticsD.1. DefinitionsD.2. Hypothesis testingReferencesIndex
£72.68
Johns Hopkins University Press An Equation for Every Occasion
Book SynopsisSmartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.Trade ReviewThe wide ranging essays touch on history, art, architecture, biology, astrophysics, geology, economics, engineering, and many aspects of everyday life. They are supplemented with helpful graphics and written in a lively and clear style appropriate for non-specialist readers, including high school students. Mathematical Reviews An intriguing, thought provoking and humorous book... Highly entertaining treatises for nature lovers as well as science, mathematics and art enthusiasts. London Mathematical Society Newsletter Henshaw's stories about each formula are interesting, humorous, and oftentimes surprising. The range of formulas in [ An Equation for Every Occasion] is appealing, no matter where one's interests lie... This book is a must for teachers who teach formulas. This book provides both interesting stories and historial context to pass on to students Mathematical Association of America From the links between music and math and the importance of the concept of friction to either the success or failure of athletes to estimating the size of a crowd by understanding principles of density, these applications are not only lively discussions of daily living, but require no prior math knowledge from their readers, making An Equation for Every Occasion a recommended pick for lay audiences interested in math's intersections with real-world concerns. Donovan's Literary Services Recommended. All readers. ChoiceTable of ContentsPreface1. As the Earth Draws the Apple2. And All the Children Are Above Average3. The Lady with the Mystic Smile4. The Heart Has Its Reasons5. AC/DC6. The Doppler Effect7. Do I Look Fat in These Jeans?8. Zeros and Ones9. Tsunami10. When the Chips Are Down11. A Stretch of the Imagination12. Woodstock Nation13. What Is (Pi)?14. No Sweat15. Road Range16. The Bends17. It's Not the Heat, It's the Humidity18. The World's Most Beautiful Equation19. Breaking the Law20. The Mars Curse21. Eureka!22. A Penny Saved . . .23. If I Only Had a Brain24. Because It Was There25. Four Eyes26. Bee Sting27. Here Comes the Sun28. A Leg to Stand On29. Love Is a Roller Coaster30. Loss Factor31. A Slippery Slope32. Transformers33. A House of Cards34. Let There Be Light35. Smarty Pants36. As Old as the Hills37. Can You Hear Me Now?38. Decay Heat39. Zero, One, Infinity40. Terminal Velocity41. Water, Water, Everywhere42. Dog Days43. Body Heat44. Red Hot45. A Bolt from the Blue46. Like Oil and Water47. Fish Story48. Making Waves49. A Drop in the Bucket50. Fracking Unbelievable51. Take Two Aspirins and Call Me in the Morning52. The World's Most Famous EquationBibliographyIndex
£26.50
Johns Hopkins University Press Tensor Calculus for Physics
Book SynopsisIt is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.Trade ReviewThis book is well written and has sufficient rigor to allow students to use it for independent study. Choice An introductory Tensor Calculus for Physics book is a most welcome addition... Professor Neuenschwander's book fills the gap in robust fashion. American Journal of PhysicsTable of ContentsPrefaceAcknowledgmentsChapter 1. Tensors Need Context1.1. Why Aren't Tensors Defined by What They Are?1.2. Euclidean Vectors, without Coordinates1.3. Derivatives of Euclidean Vectors with Respect to a Scalar1.4. The Euclidean Gradient1.5. Euclidean Vectors, with Coordinates1.6. Euclidean Vector Operations with and without Coordinates1.7. Transformation Coefficients as Partial Derivatives1.8. What Is a Theory of Relativity?1.9. Vectors Represented as Matrices1.10. Discussion Questions and ExercisesChapter 2. Two-Index Tensors2.1. The Electric Susceptibility Tensor2.2. The Inertia Tensor2.3. The Electric Quadrupole Tensor2.4. The Electromagnetic Stress Tensor2.5. Transformations of Two-Index Tensors2.6. Finding Eigenvectors and Eigenvalues2.7. Two-Index Tensor Components as Products of Vector Components2.8. More Than Two Indices2.9. Integration Measures and Tensor Densities2.10. Discussion Questions and ExercisesChapter 3. The Metric Tensor3.1. The Distinction between Distance and Coordinate Displacement3.2. Relative Motion3.3. Upper and Lower Indices3.4. Converting between Vectors and Duals3.5. Contravariant, Covariant, and "Ordinary" Vectors3.6. Tensor Algebra3.7. Tensor Densities Revisited3.8. Discussion Questions and ExercisesChapter 4. Derivatives of Tensors4.1. Signs of Trouble4.2. The Affine Connection4.3. The Newtonian Limit4.4. Transformation of the Affine Connection4.5. The Covariant Derivative4.6. Relation of the Affine Connection to the Metric Tensor4.7. Divergence, Curl, and Laplacian with Covariant Derivatives4.8. Disccussion Questions and ExercisesChapter 5. Curvature5.1. What Is Curvature?5.2. The Riemann Tensor5.3. Measuring Curvature5.4. Linearity in the Second Derivative5.5. Discussion Questions and ExercisesChapter 6. Covariance Applications6.1. Covariant Electrodynamics6.2. General Covariance and Gravitation6.3. Discussion Questions and ExercisesChapter 7. Tensors and Manifolds7.1. Tangent Spaces, Charts, and Manifolds7.2. Metrics on Manifolds and Their Tangent Spaces7.3. Dual Basis Vectors7.4. Derivatives of Basis Vectors and the Affine Connection7.5. Discussion Questions and ExercisesChapter 8. Getting Acquainted with Differential Forms8.1. Tensors as Multilinear Forms8.2. 1-Forms and Their Extensions8.3. Exterior Products and Differential Forms8.4. The Exterior Derivative8.5. An Application to Physics: Maxwell's Equations8.6. Integrals of Differential Forms8.7. Discussion Questions and ExercisesAppendix A: Common Coordinate SystemsAppendix B: Theorem of AlternativesAppendix C: Abstract Vector SpacesBibliographyIndex
£35.10
Johns Hopkins University Press An Equation for Every Occasion
Book SynopsisSmartly conceived and fast paced, his book offers something for anyone curious about math and its impacts.Trade ReviewThe wide ranging essays touch on history, art, architecture, biology, astrophysics, geology, economics, engineering, and many aspects of everyday life. They are supplemented with helpful graphics and written in a lively and clear style appropriate for non-specialist readers, including high school students. Mathematical Reviews An intriguing, thought provoking and humorous book... Highly entertaining treatises for nature lovers as well as science, mathematics and art enthusiasts. London Mathematical Society Newsletter Henshaw's stories about each formula are interesting, humorous, and oftentimes surprising. The range of formulas in [ An Equation for Every Occasion] is appealing, no matter where one's interests lie... This book is a must for teachers who teach formulas. This book provides both interesting stories and historial context to pass on to students Mathematical Association of America From the links between music and math and the importance of the concept of friction to either the success or failure of athletes to estimating the size of a crowd by understanding principles of density, these applications are not only lively discussions of daily living, but require no prior math knowledge from their readers, making An Equation for Every Occasion a recommended pick for lay audiences interested in math's intersections with real-world concerns. Donovan's Literary Services Recommended. All readers. ChoiceTable of ContentsPreface1. As the Earth Draws the Apple2. And All the Children Are Above Average3. The Lady with the Mystic Smile4. The Heart Has Its Reasons5. AC/DC6. The Doppler Effect7. Do I Look Fat in These Jeans?8. Zeros and Ones9. Tsunami10. When the Chips Are Down11. A Stretch of the Imagination12. Woodstock Nation13. What Is (Pi)?14. No Sweat15. Road Range16. The Bends17. It's Not the Heat, It's the Humidity18. The World's Most Beautiful Equation19. Breaking the Law20. The Mars Curse21. Eureka!22. A Penny Saved . . .23. If I Only Had a Brain24. Because It Was There25. Four Eyes26. Bee Sting27. Here Comes the Sun28. A Leg to Stand On29. Love Is a Roller Coaster30. Loss Factor31. A Slippery Slope32. Transformers33. A House of Cards34. Let There Be Light35. Smarty Pants36. As Old as the Hills37. Can You Hear Me Now?38. Decay Heat39. Zero, One, Infinity40. Terminal Velocity41. Water, Water, Everywhere42. Dog Days43. Body Heat44. Red Hot45. A Bolt from the Blue46. Like Oil and Water47. Fish Story48. Making Waves49. A Drop in the Bucket50. Fracking Unbelievable51. Take Two Aspirins and Call Me in the Morning52. The World's Most Famous EquationBibliographyIndex
£22.50
Johns Hopkins University Press Understanding Topology
Book SynopsisA fresh approach to topology makes this complex topic easier for students to master. Topologythe branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortionscan present significant challenges for undergraduate students of mathematics and the sciences. Understanding Topology aims to change that. The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not. This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology explains metric topTrade ReviewA perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the textbook's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles, and might reasonably be expected to become a standard reference for teaching backgrounds of topology in the years to come.—Marek Golasinski (Olsztyn), Zentralblatt MathA useful book for undergraduates, with the initial introduction to concepts being at the level of intuition and analogy, followed by mathematical rigour.—John Bartlett CMath MIMA, Mathematics TodayTable of ContentsPrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex
£80.27
Springer-Verlag New York Inc. Advanced Mathematical Methods for Scientists and
Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index
£49.49
Springer-Verlag New York Inc. Complex Analysis
This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.
£44.99
Springer-Verlag New York Inc. Advanced Calculus
Book SynopsisWith a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse''s lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.Trade ReviewFrom the reviews:“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)Table of Contents1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises
£53.09
Springer Science+Business Media An Introduction to Manifolds
Book SynopsisManifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.Trade ReviewFrom the reviews of the second edition:“This book could be called a prequel to the book ‘Differential forms in algebraic topology’ by R. Bott and the author. Assuming only basic background in analysis and algebra, the book offers a rather gentle introduction to smooth manifolds and differential forms offering the necessary background to understand and compute deRham cohomology. … The text also contains many exercises … for the ambitious reader.” (A. Cap, Monatshefte für Mathematik, Vol. 161 (3), October, 2010)Table of ContentsPreface to the Second Edition.- Preface to the First Edition.-Chapter 1. Eudlidean Spaces. 1. Smooth Functions on a Euclidean Space.- 2. Tangent Vectors in R(N) as Derivativations.- 3. The Exterior Algebra of Multicovectors.- 4. Differential Forms on R(N).- Chapter 2. Manifolds.- 5. Manifolds.- 6. Smooth Maps on a Manifold.- 7. Quotients.- Chapter 3. The Tangent Space.- 8. The Tangent Space.- 9. Submanifolds.- 10. Categories and Functors.- 11. The Rank of a Smooth Map.- 12. The Tangent Bundle.- 13. Bump Functions and Partitions of Unity.- 14. Vector Fields.-Chapter 4. Lie Groups and Lie Algebras.- 15. Lie Groups.- 16. Lie Algebras.- Chapter 5. Differential Forms.- 17. Differential 1-Forms.- 18. Differential k-Forms.- 19. The Exterior Derivative.- 20. The Lie Derivative and Interior Multiplication.- Chapter 6. Integration.- 21. Orientations.- 22. Manifolds with Boundary.- 23. Integration on Manifolds.- Chapter 7. De Rham Theory.- 24. De Rham Cohomology.- 25. The Long Exact Sequence in Cohomology.- 26. The Mayer –Vietoris Sequence.- 27. Homotopy Invariance.- 28. Computation of de Rham Cohomology.- 29. Proof of Homotopy Invariance.-Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.
£42.74
Pearson Education College Algebra MyLab Math without Pearson eText
Book Synopsis
£58.28
Springer New York Introduction to Spectral Theory With Applications to Schrdinger Operators Applied Mathematical Sciences 113
Book Synopsis1 The Spectrum of Linear Operators and Hilbert Spaces.- 2 The Geometry of a Hilbert Space and Its Subspaces.- 3 Exponential Decay of Eigenfunctions.- 4 Operators on Hilbert Spaces.- 5 Self-Adjoint Operators.- 6 Riesz Projections and Isolated Points of the Spectrum.- 7 The Essential Spectrum: Weyl's Criterion.- 8 Self-Adjointness: Part 1. The Kato Inequality.- 9 Compact Operators.- 10 Locally Compact Operators and Their Application to Schrödinger Operators.- 11 Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation.- 12 Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues.- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131.- 14 Relatively Compact Operators and the Weyl Theorem.- 15 Perturbation Theory: Relatively Bounded Perturbations.- 16 Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem.- 17 Spectral Deformation Theory.- 18 Spectral Deformation of Schrödinger Operators.- 19 The General Theory of Spectral Stability.- 20 Theory of Quantum Resonances II: The Shape Resonance Model.- 21 Quantum Nontrapping Estimates.- 22 Theory of Quantum Resonances III: Resonance Width.- 23 Other Topics in the Theory of Quantum Resonances.- Appendix 1. Introduction to Banach Spaces.- A1.1 Linear Vector Spaces and Norms.- A1.2 Elementary Topology in Normed Vector Spaces.- A1.3 Banach Spaces.- A1.4 Compactness.- 1. Density results.- 2. The Hölder Inequality.- 3. The Minkowski Inequality.- 4. Lebesgue Dominated Convergence.- Appendix 3. Linear Operators on Banach Spaces.- A3.1 Linear Operators.- A3.2 Continuity and Boundedness of Linear Operators.- A3.3 The Graph of an Operator and Closure.- A3.4 Inverses of Linear Operators.- A3.5 Different Topologies on L(X).- Appendix 4. The Fourier Transform, SobolevSpaces, and Convolutions.- A4.1 Fourier Transform.- A4.2 Sobolev Spaces.- A4.3 Convolutions.- References.Table of Contents1 The Spectrum of Linear Operators and Hilbert Spaces.- 2 The Geometry of a Hilbert Space and Its Subspaces.- 3 Exponential Decay of Eigenfunctions.- 4 Operators on Hilbert Spaces.- 5 Self-Adjoint Operators.- 6 Riesz Projections and Isolated Points of the Spectrum.- 7 The Essential Spectrum: Weyl’s Criterion.- 8 Self-Adjointness: Part 1. The Kato Inequality.- 9 Compact Operators.- 10 Locally Compact Operators and Their Application to Schrödinger Operators.- 11 Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation.- 12 Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues.- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131.- 14 Relatively Compact Operators and the Weyl Theorem.- 15 Perturbation Theory: Relatively Bounded Perturbations.- 16 Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem.- 17 Spectral Deformation Theory.- 18 Spectral Deformation of Schrödinger Operators.- 19 The General Theory of Spectral Stability.- 20 Theory of Quantum Resonances II: The Shape Resonance Model.- 21 Quantum Nontrapping Estimates.- 22 Theory of Quantum Resonances III: Resonance Width.- 23 Other Topics in the Theory of Quantum Resonances.- Appendix 1. Introduction to Banach Spaces.- A1.1 Linear Vector Spaces and Norms.- A1.2 Elementary Topology in Normed Vector Spaces.- A1.3 Banach Spaces.- A1.4 Compactness.- 1. Density results.- 2. The Hölder Inequality.- 3. The Minkowski Inequality.- 4. Lebesgue Dominated Convergence.- Appendix 3. Linear Operators on Banach Spaces.- A3.1 Linear Operators.- A3.2 Continuity and Boundedness of Linear Operators.- A3.3 The Graph of an Operator and Closure.- A3.4 Inverses of Linear Operators.- A3.5 Different Topologies on L(X).- Appendix 4. The Fourier Transform, Sobolev Spaces, and Convolutions.- A4.1 Fourier Transform.- A4.2 Sobolev Spaces.- A4.3 Convolutions.- References.
£189.99
Springer Nonlinear Functional Analysis and its Applications
Book SynopsisFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 2 The Schauder Fixed-Point Theorem and Compactness.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- 4 Differential Calculus and the Implicit Function Theorem.- 5 Newton's Method.- 6 Continuation with Respect to a Parameter.- 7 Positive Operators.- 8 Analytic Bifurcation Theory.- 9 Fixed Points of Multivalued Maps.- 10 Nonexpansive Operators and Iterative Methods.- 11 Condensing Maps and the BourbakiKneser Fixed-Point Theorem.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- 13 Applications of the Fixed-Point Index.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- 15 Topological Bifurcation Theory.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- 17 Asymptotic Fixed-Point Theorems.- References.- Additional References to the Second Printing.- List of Symbols.- List of TheoreTable of ContentsFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- §1.1. The Banach Fixed-Point Theorem.- §1.2. Continuous Dependence on a Parameter.- §1.3. The Significance of the Banach Fixed-Point Theorem.- §1.4. Applications to Nonlinear Equations.- §1.5. Accelerated Convergence and Newton’s Method.- § 1.6. The Picard-Lindelof Theorem.- §1.7. The Main Theorem for Iterative Methods for Linear Operator Equations.- §1.8. Applications to Systems of Linear Equations.- §1.9. Applications to Linear Integral Equations.- 2 The Schauder Fixed-Point Theorem and Compactness.- §2.1. Extension Theorem.- §2.2. Retracts.- §2.3. The Brouwer Fixed-Point Theorem.- §2.4. Existence Principle for Systems of Equations.- §2.5. Compact Operators.- §2.6. The Schauder Fixed-Point Theorem.- §2.7. Peano’s Theorem.- §2.8. Integral Equations with Small Parameters.- §2.9. Systems of Integral Equations and Semilinear Differential Equations.- §2.10. A General Strategy.- §2.11. Existence Principle for Systems of Inequalities.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- §3.1. Integration of Vector Functions of One Real Variable t.- §3.2. Differentiation of Vector Functions of One Real Variable t.- §3.3. Generalized Picard-Lindelöf Theorem.- §3.4. Generalized Peano Theorem.- §3.5. Gronwall’s Lemma.- §3.6. Stability of Solutions and Existence of Periodic Solutions.- §3.7. Stability Theory and Plane Vector Fields, Electrical Circuits, Limit Cycles.- §3.8. Perspectives.- 4 Differential Calculus and the Implicit Function Theorem.- §4.1. Formal Differential Calculus.- §4.2. The Derivatives of Fréchet and Gâteaux.- §4.3. Sum Rule, Chain Rule, and Product Rule.- §4.4. Partial Derivatives.- §4.5. Higher Differentials and Higher Derivatives.- §4.6. Generalized Taylor’s Theorem.- §4.7. The Implicit Function Theorem.- §4.8. Applications of the Implicit Function Theorem.- §4.9. Attracting and Repelling Fixed Points and Stability.- §4.10. Applications to Biological Equilibria.- §4.11. The Continuously Differentiable Dependence of the Solutions of Ordinary Differential Equations in B-spaces on the Initial Values and on the Parameters.- §4.12. The Generalized Frobenius Theorem and Total Differential Equations.- §4.13. Diffeomorphisms and the Local Inverse Mapping Theorem.- §4.14. Proper Maps and the Global Inverse Mapping Theorem.- §4.15. The Suijective Implicit Function Theorem.- §4.16. Nonlinear Systems of Equations, Subimmersions, and the Rank Theorem.- §4.17. A Look at Manifolds.- §4.18. Submersions and a Look at the Sard-Smale Theorem.- §4.19. The Parametrized Sard Theorem and Constructive Fixed-Point Theory.- 5 Newton’s Method.- §5.1. A Theorem on Local Convergence.- §5.2. The Kantorovi? Semi-Local Convergence Theorem.- 6 Continuation with Respect to a Parameter.- §6.1. The Continuation Method for Linear Operators.- §6.2. B-spaces of Hölder Continuous Functions.- §6.3. Applications to Linear Partial Differential Equations.- §6.4. Functional-Analytic Interpretation of the Existence Theorem and its Generalizations.- §6.5. Applications to Semi-linear Differential Equations.- §6.6. The Implicit Function Theorem and the Continuation Method.- §6.7. Ordinary Differential Equations in B-spaces and the Continuation Method.- §6.8. The Leray—Schauder Principle.- §6.9. Applications to Quasi-linear Elliptic Differential Equations.- 7 Positive Operators.- §7.1. Ordered B-spaces.- §7.2. Monotone Increasing Operators.- §7.3. The Abstract Gronwall Lemma and its Applications to Integral Inequalities.- §7.4. Supersolutions, Subsolutions, Iterative Methods, and Stability.- §7.5. Applications.- §7.6. Minorant Methods and Positive Eigensolutions.- §7.7. Applications.- §7.8. The Krein-Rutman Theorem and its Applications.- §7.9. Asymptotic Linear Operators.- §7.10. Main Theorem for Operators of Monotone Type.- §7.11. Application to a Heat Conduction Problem.- §7.12. Existence of Three Solutions.- §7.13. Main Theorem for Abstract Hammerstein Equations in Ordered B-spaces.- §7.14. Eigensolutions of Abstract Hammerstein Equations, Bifurcation, Stability, and the Nonlinear Krein-Rutman Theorem.- §7.15. Applications to Hammerstein Integral Equations.- §7.16. Applications to Semi-linear Elliptic Boundary-Value Problems.- §7.17. Application to Elliptic Equations with Nonlinear Boundary Conditions.- §7.18. Applications to Boundary Initial-Value Problems for Parabolic Differential Equations and Stability.- 8 Analytic Bifurcation Theory.- §8.1. A Necessary Condition for Existence of a Bifurcation Point.- §8.2. Analytic Operators.- §8.3. An Analytic Majorant Method.- §8.4. Fredholm Operators.- §8.5. The Spectrum of Compact Linear Operators (Riesz—Schauder Theory).- §8.6. The Branching Equations of Ljapunov—Schmidt.- §8.7. The Main Theorem on the Generic Bifurcation From Simple Zeros.- §8.8. Applications to Eigenvalue Problems.- §8.9. Applications to Integral Equations.- §8.10. Application to Differential Equations.- §8.11. The Main Theorem on Generic Bifurcation for Multiparametric Operator Equations—The Bunch Theorem.- §8.12. Main Theorem for Regular Semi-linear Equations.- §8.13. Parameter-Induced Oscillation.- §8.14. Self-Induced Oscillations and Limit Cycles.- §8.15. Hopf Bifurcation.- §8.16. The Main Theorem on Generic Bifurcation from Multiple Zeros.- §8.17. Stability of Bifurcation Solutions.- §8.18. Generic Point Bifurcation.- 9 Fixed Points of Multivalued Maps.- §9.1. Generalized Banach Fixed-Point Theorem.- §9.2. Upper and Lower Semi-continuity of Multivalued Maps.- §9.3. Generalized Schauder Fixed-Point Theorem.- §9.4. Variational Inequalities and the Browder Fixed-Point Theorem.- §9.5. An Extremal Principle.- §9.6. The Minimax Theorem and Saddle Points.- §9.7. Applications in Game Theory.- §9.8. Selections and the Marriage Theorem.- §9.9. Michael’s Selection Theorem.- §9.10. Application to the Generalized Peano Theorem for Differential Inclusions.- 10 Nonexpansive Operators and Iterative Methods.- §10.1. Uniformly Convex B-spaces.- §10.2. Demiclosed Operators.- §10.3. The Fixed-Point Theorem of Browder, Göhde, and Kirk.- §10.4. Demicompact Operators.- §10.5. Convergence Principles in B-spaces.- §10.6. Modified Successive Approximations.- §10.7. Application to Periodic Solutions.- 11 Condensing Maps and the Bourbaki—Kneser Fixed-Point Theorem.- §11.1. A Noncompactness Measure.- §11.2. Applications to Generalized Interval Nesting.- §11.3. Condensing Maps.- §11.4. Operators with Closed Range and an Approximation Technique for Constructing Fixed Points.- §11.5. Sadovskii’s Fixed-Point Theorem for Condensing Maps.- §11.6. Fixed-Point Theorems for Perturbed Operators.- §11.7. Application to Differential Equations in B-spaces.- §11.8. The Bourbaki-Kneser Fixed-Point Theorem.- § 11.9. The Fixed-Point Theorems of Amann and Tarski.- §11.10. Application to Interval Arithmetic.- §11.11. Application to Formal Languages.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- §12.1. Intuitive Background and Basic Concepts.- §12.2. Homotopy.- §12.3. The System of Axioms.- §12.4. An Approximation Theorem.- §12.5. Existence and Uniqueness of the Fixed-Point Index in ?N.- §12.6. Proof of Theorem 12.A..- §12.7. Existence and Uniqueness of the Fixed-Point Index in B-spaces.- §12.8. Product Theorem and Reduction Theorem.- 13 Applications of the Fixed-Point Index.- §13.1. A General Fixed-Point Principle.- §13.2. A General Eigenvalue Principle.- §13.3. Existence of Multiple Solutions.- §13.4. A Continuum of Fixed Points.- §13.5. Applications to Differential Equations.- §13.6. Properties of the Mapping Degree.- §13.7. The Leray Product Theorem and Homeomorphisms.- §13.8. The Jordan-Brouwer Separation Theorem and Brouwer’s Invariance of Dimension Theorem.- §13.9. A Brief Glance at the History of Mathematics.- §13.10. Topology and Intuition.- §13.11. Generalization of the Mapping Degree.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- §14.1. The Fixed-Point Index of Classical Analytic Functions.- §14.2. The Leray—Schauder Index Theorem.- §14.3. The Fixed-Point Index of Analytic Mappings on Complex B-spaces.- §14.4. The Schauder Fixed-Point Theorem with Uniqueness.- §14.5. Solution of Analytic Operator Equations.- §14.6. The Global Continuation Principle of Leray—Schauder.- §14.7. Unbounded Solution Components.- §14.8. Applications to Systems of Equations.- §14.9. Applications to Integral Equations.- §14.10. Applications to Boundary-Value Problems.- §14.11. Applications to Integral Power Series.- 15 Topological Bifurcation Theory.- §15.1. The Index Jump Principle.- §15.2. Applications to Systems of Equations.- §15.3. Duality Between the Index Jump Principle and the Leray—Schauder Continuation Principle.- §15.4. The Geometric Heart of the Continuation Method.- §15.5. Stability Change and Bifurcation.- §15.6. Local Bifurcation.- §15.7. Global Bifurcation.- §15.8. Application to Systems of Equations.- §15.9. Application to Integral Equations.- §15.10. Application to Differential Equations.- §15.11. Application to Bifurcation at Infinity.- §15.12. Proof of the Main Theorem.- §15.13. Preventing Secondary Bifurcation.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- §16.1. Intuitive Introduction.- §16.2. Essential Mappings and their Homotopy Invariance.- §16.3. The Antipodal Theorem.- §16.4. The Invariance of Domain Theorem and Global Homeomorphisms.- §16.5. The Borsuk—Ulam Theorem and its Applications.- §16.6. The Mapping Degree and Essential Maps.- §16.7. The Hopf Theorem.- §16.8. A Glance at Homotopy Theory.- 17 Asymptotic Fixed-Point Theorems.- §17.1. The Generalized Banach Fixed-Point Theorem.- §17.2. The Fixed-Point Index of Iterated Mappings.- §17.3. The Generalized Schauder Fixed-Point Theorem.- §17.4. Application to Dissipati ve Dynamical Systems.- §17.5. Perspectives.- References.- Additional References to the Second Printing.- List of Symbols.- List of Theorems.- List of the Most Important Definitions.- Schematic Overviews.- General References to the Literature.- List of Important Principles.- of the Other Parts.
£223.99
Springer-Verlag New York Inc. Ramanujans Lost Notebook Part IV
Book SynopsisIts discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series.Table of ContentsPreface.- 1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums.- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions.- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series.- 13 A Partial Manuscript on Fourier and Laplace Transforms.- 14 Integral Analogues of Theta Functions adn Gauss Sums.- 15 Functional Equations for Products of Mellin Transforms.- 16 Infinite Products.- 17 A Preliminary Version of Ramanujan's Paper, On the Integral ∫_0^x tan^(-1)t)/t dt.- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis.- 20 Elementary Results.- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide.- Provenance.- References.- Index.
£116.99
Springer-Verlag New York Inc. Elementary Analysis
Book SynopsisPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.Trade ReviewFrom the reviews of the first edition:"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."—MATHEMATICAL REVIEWS"This book occupies a niche between a calculus course and a full-blown real analysis course. … I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis … . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails." —Allen Stenger (The Mathematical Association of America, June, 2008)Table of ContentsPreface.- 1 Introduction.- 2 Sequences.- 3 Continuity.- 4 Sequences and Series of Functions.- 5 Differentiation.- 6 Integration.- 7 Capstone.- Appendix on Set Notation.- Selected Hints and Answers.- References.- Index.
£36.89
Springer-Verlag New York Inc. Measure Integral Derivative
Book SynopsisFeaturing over 180 exercises, this text for a one-semester course in Lebesgue's theory takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students.Trade ReviewFrom the reviews:“It is accessible to upper-undergraduate and lower graduate level students, and the only prerequisite is a course in elementary real analysis. … The book proposes 187 exercises where almost always the reader is proposed to prove a statement. … this book is a very helpful tool to get into Lebesgue’s theory in an easy manner.” (Daniel Cárdenas-Morales, zbMATH, Vol. 1277, 2014)“This is a brief … but enjoyable book on Lebesgue measure and Lebesgue integration at the advanced undergraduate level. … The presentation is clear, and detailed proofs of all results are given. … The book is certainly well suited for a one-semester undergraduate course in Lebesgue measure and Lebesgue integration. In addition, the long list of exercises provides the instructor with a useful collection of homework problems. Alternatively, the book could be used for self-study by the serious undergraduate student.” (Lars Olsen, Mathematical Reviews, December, 2013)Table of Contents1 Preliminaries.- 2 Lebesgue Measure.- 3 Lebesgue Integration.- 4 Differentiation and Integration.- A Measure and Integral over Unbounded Sets.- Index.
£49.49
Springer First Steps in Differential Geometry
Book SynopsisBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.Trade ReviewFrom the book reviews:“This books presents an alternative route, aiming to provide the student with an introduction not only to Riemannian geometry, but also to contact and symplectic geometry. … the book is leavened with an excellent collection of illustrative examples, and a wealth of exercises on which students can hone their skills. Each chapter also includes a short guide to further reading on the topic with a helpful brief commentary on the suggestions.” (Robert J. Low, Mathematical Reviews, May, 2014)“This book is a distinctive and ambitious effort to bring modern notions of differential geometry to undergraduates. … Mclnerney’s writing is well constructed and very clear … . Summing Up: Recommended. Upper-division undergraduates and graduate students.” (S. J. Colley, Choice, Vol. 51 (8), April, 2014)“The author does make a considerable effort to keep things as accessible as possible, with fairly detailed explanations, extensive motivational discussions and homework problems … . this book provides a different way of looking at the subject of differential geometry, one that is more modern and sophisticated than is provided by many of the standard undergraduate texts and which will certainly do a good job of preparing the student for additional work in this area down the road.” (Mark Hunacek, MAA Reviews, January, 2014)“This text provides an early and broad view of geometry to mathematical students … . Altogether, this book is easy to read because there are plenty of figures, examples and exercises which make it intuitive and perfect for undergraduate students.” (Teresa Arias-Marco, zbMATH, Vol. 1283, 2014)Table of ContentsBasic Objects and Notation.- Linear Algebra Essentials.- Advanced Calculus.- Differential Forms and Tensors.- Riemannian Geometry.- Contact Geometry.- Symplectic Geometry.- References.- Index.
£51.29
Springer Functions of Several Variables
Book Synopsis1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4Table of Contents1 Euclidean spaces.- 1.1 The real number system.- 1.2 Euclidean En.- 1.3 Elementary geometry of En.- 1.4 Basic topological notions in En.- *1.5 Convex sets.- 2 Elementary topology of En.- 2.1 Functions.- 2.2 Limits and continuity of transformations.- 2.3 Sequences in En.- 2.4 Bolzano-Weierstrass theorem.- 2.5 Relative neighborhoods, continuous transformations.- 2.6 Topological spaces.- 2.7 Connectedness.- 2.8 Compactness.- 2.9 Metric spaces.- 2.10 Spaces of continuous functions.- *2.11 Noneuclidean norms on En.- 3 Differentiation of real-valued functions.- 3.1 Directional and partial derivatives.- 3.2 Linear functions.- **3.3 Difierentiable functions.- 3.4 Functions of class C(q).- 3.5 Relative extrema.- *3.6 Convex and concave functions.- 4 Vector-valued functions of several variables.- 4.1 Linear transformations.- 4.2 Affine transformations.- 4.3 Differentiable transformations.- 4.4 Composition.- 4.5 The inverse function theorem.- 4.6 The implicit function theorem.- 4.7 Manifolds.- 4.8 The multiplier rule.- 5 Integration.- 5.1 Intervals.- 5.2 Measure.- 5.3 Integrals over En.- 5.4 Integrals over bounded sets.- 5.5 Iterated integrals.- 5.6 Integrals of continuous functions.- 5.7 Change of measure under affine transformations.- 5.8 Transformation of integrals.- 5.9 Coordinate systems in En.- 5.10 Measurable sets and functions; further properties.- 5.11 Integrals: general definition, convergence theorems.- 5.12 Differentiation under the integral sign.- 5.13 Lp-spaces.- 6 Curves and line integrals.- 6.1 Derivatives.- 6.2 Curves in En.- 6.3 Differential 1-forms.- 6.4 Line integrals.- *6.5 Gradient method.- *6.6 Integrating factors; thermal systems.- 7 Exterior algebra and differential calculus.- 7.1 Covectors and differential forms of degree 2.- 7.2 Alternating multilinear functions.- 7.3 Multicovectors.- 7.4 Differential forms.- 7.5 Multivectors.- 7.6 Induced linear transformations.- 7.7 Transformation law for differential forms.- 7.8 The adjoint and codifferential.- *7.9 Special results for n = 3.- *7.10 Integrating factors (continued).- 8 Integration on manifolds.- 8.1 Regular transformations.- 8.2 Coordinate systems on manifolds.- 8.3 Measure and integration on manifolds.- 8.4 The divergence theorem.- *8.5 Fluid flow.- 8.6 Orientations.- 8.7 Integrals of r-forms.- 8.8 Stokes’s formula.- 8.9 Regular transformations on submanifolds.- 8.10 Closed and exact differential forms.- 8.11 Motion of a particle.- 8.12 Motion of several particles.- Axioms for a vector space.- Mean value theorem; Taylor’s theorem.- Review of Riemann integration.- Monotone functions.- References.- Answers to problems.
£51.29
MP-AMM American Mathematical Pearls from a Lost City
Book SynopsisTrade ReviewMany journal articles have been devoted to various aspects of mathematics in Lvov or to biographies of Lvov mathematicians, but Duda's book is the first comprehensive exposition...In summary, I conclude that Duda's book is a must for everyone interested in the history of functional analysis or in the history of mathematics in Poland." - Lech Maligranda, Mathematical Intelligencer"This eagerly awaited translation of the book Pearls describes a world-class Polish school of mathematics at Lvov (now the Ukrainian Lviv) that thrived during the interwar period and has left an enduring legacy that remains part of the folklore today. Published in English translation after a somewhat protracted period of negotiation, this important work fills a niche in the history of science and should become a standard source of mathematics in Poland, especially the genesis of functional analysis during its Golden Age, 1918-1939. Moreover, the translator, Oxford's Daniel Davies, explains material that is unlikely to be familiar to readers outside Poland." - Isis, A Journal of the History of Science Society"Many journal articles have been devoted to various aspects of mathematics in Lwów or to biographies of Lwów mathematicians, but Duda's book is the first comprehensive exposition. It is a must-read for everyone interested in the history of functional analysis or of mathematics in Poland, where the original Polish edition from 2007 ... has been highly successful. There is good reason to assume that the English version will be likewise successful." - Dirk Werner, ZMATH"This book gives the history of Lvov as a mathematical center, from pre-WWI to Soviet and Ukrainian times, looking especially at the interwar golden age and the special favorable environment for mathematical scholarship. The author also describes the ways in which the Soviets and Germans destroyed this rich environment. The book includes a list, with biographical sketches, of mathematicians associated with Lvov, and a Lvov biography. It was a special time and place for mathematics, disrupted by war and politics and oppression and murder, and one wonders what more could have been achieved in a peaceful environment." - CHOICE Reviews"The book under review is well and carefully written. The translation from Polish into English is polished and lively... I highly recommend the book for all university libraries, and I recommend it to those interested in the history of mathematics. The general mathematical reader will find it an entertaining and informative story about mathematicians and a truly extraordinary mathematical community." - Henry Heatherly, MAA ReviewsTable of Contents Background The University and the Polytechnic in Lvov Polish mathematics at the turn of the twentieth century Sierpiski's stay at the University of Lvov (1908-1914) The University in Warsaw and Janiszewski's program (1915-1920) World mathematics (active fields in Poland) around 1920 The golden age: Individuals and community The mathematical community in Lvov after World War I Mathematical studies and students Journals, monographs, and congresses The popularization of mathematics Social life (the Scottish Café, the Scottish Book) The Polish Mathematical Society Collaboration with other centers In the eyes of others The golden age: Achievements Stefan Banach's doctoral thesis and priority claims Probability theory Measure theory Game theory: A revelation without follow-up Operator theory in the 1920s Methodological audacity Banach's monograph: Polishing the pearls Operator theory in the 1930s: The dazzle of pearls New perspectives for which time did not allow On the periphery Oblivion Ukrainization the Soviet way (1939-1941) The German occupation (1941-1944) The expulsion of Poles (1945-1946) Historical significance Chronological overview Chronology of events as perceived elsewhere Influence on mathematics of the Lvov school A tentative summary Mathematics in Lvov after 1945 List of Lvov mathematicians Mathematicians associated with Lvov Bibliographies List of illustrations Index of names
£99.90
MP-AMM American Mathematical Differentiable Dynamical Systems An Introduction
Book SynopsisTrade ReviewThis book introduces the reader to some basic concepts of hyperbolic theory of dynamical systems with emphasis on structural stability. It is well written, the proofs are presented with great attention to details, and every chapter ends with a good collection of exercises. It is suitable for a semester-long course on the basics of dynamical systems"". - Yakov Pesin, Penn State University""Lan Wen's book is a thorough introduction to the ``classical'' theory of (uniformly) hyperbolic dynamics, updated in light of progress since Smale's seminal 1967 Bulletin article. The exposition is aimed at newcomers to the field and is clearly informed by the author's extensive experience teaching this material. A thorough discussion of some canonical examples and basic technical results culminates in the proof of the Omega-stability theorem and a discussion of structural stability. A fine basic text for an introductory dynamical systems course at the graduate level"". - Zbigniew Nitecki, Tufts University"...[T]he introductory parts of the book are quite suitable for graduate students, and the more advanced sections can be useful even for experts in the field." - S. Yu. Pilyugin, Mathematical ReviewsTable of Contents Basics of dynamical systems Hyperbolic fixed points Horseshoes, toral automorphisms, and solenoids Hyperbolic sets Axiom A, no-cycle condition, and Ω-stability Quasi-hyperbolicity and linear transversality Bibliography Index
£108.00
MP-AMM American Mathematical Mathematical Biology
Book SynopsisConsiders models that are described by systems of partial differential equations, focusing on modelling rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing.Table of Contents Introductory biology Introduction to modeling Models of population dynamics Cancer and the immune system Parameters estimation Mathematical analysis inspired by cancer models Mathematical model of artherosclerosis: Risk of high cholesterol Mathematical analysis inspired by the atherosclerosis model Mathematical models of chronic wounds Mathematical analysis inspired by the chronic wound model Introduction to PDEs Bibliography Index
£44.06
MP-AMM American Mathematical Analytic Trends in Mathematical Physics
Book SynopsisThis volume contains the proceedings of the “Arizona School of Analysis and Mathematical Physics”, held in March 2018, at the University of Arizona. The articles in this volume reflect recent progress and innovative techniques developed within mathematical physics.Table of Contents H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young, A class of two-dimensional AKLT models with a gap S. Bachmann, A. Bols, W. De Roeck, and M. Fraas, Note on linear response for interacting Hall insulators S. Bachmann, W. De Roeck, and M. Fraas, The adiabatic theoerm in a quantum many-body setting R. DeMuse and M. Yin, Perspectives on exponential random graphs C. Fischbacher, A Schrodinger operator approach to higher spin XXZ systems on general graphs Y. Latushkin and S. Sukhtaiev, An index theorem for Schrodinger operators on metric graphs M. Lemm, Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems A. Saenz, The KPZ universality class and related topics G. Stolz, Aspects of the mathematical theory of disordered quantum spin chains.
£94.50
MP-AMM American Mathematical Linear and Quasilinear Parabolic Systems Sobolev
Book SynopsisPresents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients.Table of Contents Introduction Differential equations in Hilbert space Linear parabolic systems: Basic theory Elliptic systems: Higher order regularity Parabolic systems: Higher order regularity Applications to quasilinear systems Selected topics in analysis Bibliography Index
£109.80
MP-AMM American Mathematical Complex Function Theory
Book SynopsisProvides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.Trade ReviewFrom a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —Zentralblatt MATHTable of Contents Complex numbers Complex differentiation Linear-fractional transformations Elementary functions Power series Complex integration Core versions of Cauchy's theorem, and consequences Laurent series and isolated singularities Cauchy's theorem Further development of basic complex function theory Appendix 1: Sufficient condition for differentiability Appendix 2: Two instances of the chain rule Appendix 3: Groups, and linear-fractional transformations Appendix 4: Differentiation under the integral sign References Index
£38.66
MP-AMM American Mathematical Analytic Number Theory for Beginners
Book SynopsisPresents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes.Table of Contents Review of elementary number theory Arithmetic functions I The floor function Summation formulas Arithmetic functions II Elementary results on the distribution of primes Characters and Dirichlet's theorem The Riemann zeta function Prime number theorem and some extensions Introduction to other topics Hints for selected exercises Bibliography Subject index Name Index
£46.50
MP-AMM American Mathematical Applied Stochastic Analysis
Book SynopsisPresents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events).Trade ReviewThis book strikes a nice balance between mathematical formalism and intuitive arguments; a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation."" —Peter Rabinovitch, MAA Reviews Table of Contents Fundamentals: Random variables Limit theorems Markov chains Monte Carlo methods Stochastic processes Wiener process Stochastic differential equations Fokker-Planck equation Advanced topics: Path integral Random fields Introduction to statistical mechanics Rare events Introduction to chemical reaction kinetics Appendix Bibliography Index
£70.20
MP-AMM American Mathematical Recent Trends in Formal and Analytic Solutions of
Book SynopsisCovers recent advances in the study of formal and analytic solutions of different kinds of equations such as ordinary differential equations, difference equations, $q$-difference equations, partial differential equations, and moment differential equations.Table of Contents A. D. Bruno, Normal forms of a polynomial ODE A. B. Batkhin, Computation of homological equations for Hamiltonian normal form E. Ciechanowicz, A note on value distribution of solutions of certain second order ODEs G. Filipuk, A. Ligeza, and A. Stokes, Relations between different Hamiltonian forms of the third Painleve equation T. Aoki and S. Uchida, Degeneration structures of the Voros coefficients of the generalized hypergeometric differential equations with a large parameter T. Oshima, Riemann-Liouville transform and linear differential equations on the Riemann sphere M. Cafasso and S. Tarricone, The Riemann-Hilbert approach to the generating function of the higher order Airy point processes Y. Chen, G. Filipuk, and M. N. R. Rebocho, A system of nonlinear difference equations for recurrence relation coefficients of a modified Jacobi weight S. Sasaki, S. Takagi, and K. Takemura, $q$-Heun equation and initial-value space of $q$-Painleve equation H. Ogawara, Differential transcendence of solutions for $q$-difference equation of Ramanujan function C. Zhang, On the positive powers of $q$-analogs of Euler series M. Suwinska, Summability of formal solutions for a family of linear moment integro-differential equations H. Tahara, Uniqueness of the solution of some nonlinear singular partial differential equations of the second order M. Yoshino, Solution with movable singular points of some Hamiltonian system A. Lastra, S. Michalik, and M. Suwinska, Some notes on moment partial differential equations. Application to fractional functional equations.
£102.60
MP-AMM American Mathematical SYZ Geometry for CalabiYau 3folds TaubNUT and
Book Synopsis
£68.40
