Mathematics Books

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Book SynopsisWhile trying to save enough money to buy a new ice scooter, Perry the Penguin learns about managing his money and about negative numbers.

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Book SynopsisTrade Review"Data Science for Business and Decision Making brings together the key topics required as the foundation for understanding and applying analytics for decision making. The authors have carefully selected the topics, and each one is clearly explained, described, and reinforced with a diverse set of exercises." --Rahul Saxena, Cobot Systems "Data Science for Business and Decision Making provides a thorough essay about statistical methods which are commonly used in business without requiring a strong mathematical background. The presentation is rigorous and accessible thanks to a large number of examples that are developed step-by-step. The illustrations feature various software and the proposed exercises are particularly helpful for students and practitioners." --Francesco Bartolucci, University of PerugiaTable of ContentsPart 1: Foundations of Business Data Analysis 1. Introduction to Data Analysis and Decision Making 2. Type of Variables and Mensuration Scales Part 2: Descriptive Statistics 3. Univariate Descriptive Statistics 4. Bivariate Descriptive Statistics Part 3: Probabilistic Statistics 5. Introduction of Probability 6. Random Variables and Probability Distributions Part 4: Statistical Inference 7. Sampling 8. Estimation 9. Hypothesis Tests 10. Non-parametric Tests Part 5: Multivariate Exploratory Data Analysis 11. Cluster Analysis 12. Principal Components Analysis and Factorial Analysis Part 6: Generalized Linear Models 13. Simple and Multiple Regression Models 14. Binary and Multinomial Logistics Regression Models 15. Regression Models for Count Data: Poisson and Negative Binomial Part 7: Optimization Models and Simulation 16. Introduction to Optimization Models: Business Problems Formulations and Modeling 17. Solution of Linear Programming Problems 18. Network Programming 19. Integer Programming 20. Simulation and Risk Analysis Part 8: Other Topics 21. Design and Experimental Analysis 22. Statistical Process Control 23. Data Mining and Multilevel Modeling

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Book SynopsisTable of Contents1. Planning Studies: From Design to Publication 2. Planning Analysis: Addressing Your Scientific Objective 3. Probability and Relative Frequency 4. Distributions 5. Descriptive Statistics 6. Finding Probabilities 7. Hypothesis Testing: Concept and Practice 8. Confidence Intervals 9. Tests on Categorical Data 10. Risks, Odds, and ROC Curves 11. Tests of Location with Continuous Outcomes 12. Equivalence Testing 13. Tests on Variability and Distributions 14. Measuring Association and Agreement 15. Linear Regression and Correlation 16. Multiple Linear and Curvilinear Regression 17. Logistic Regression for Binary Outcomes 18. Regression Models for Count Outcomes 19. Analysis of Censored Time-To-Event Data 20. Analysis of Repeated Continuous Measures of Time 21. Sample Size Estimation 22. Clinical Trials and Group Sequential Analyses 23. Epidemiology and Alternative Sampling Designs 24. Meta Analyses 25. Bayesian Statistics 26. Questionnaires and Surveys 27. Techniques to Aid Analysis 28. Methods You Might Meet, But Not Every Day

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Book SynopsisTable of ContentsPart 1. MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices (Arrays) 3. Plotting in MATLAB 4. Three-Dimensional Plots 5. Functions 6. Control Flow 7. Miscellaneous Commands and Code Improvement Part 2. Mathematics and MATLAB 8. Transformations and Fern Fractals 9. Complex Numbers and Fractals 10. Series and Taylor Polynomials 11. Numerical Integration 12. The Gram–Schmidt Process Appendices A. Publishing and Live Scripts B. Final Projects C. Linear Algebra Projects D. Multivariable Calculus Projects

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Book SynopsisTable of Contents1. Matrices 2. Simultaneous linear equations 3. The inverse 4. An introduction to optimization 5. Determinants 6. Eigenvalues and eigenvectors 7. Matrix calculus 8. Linear differential equations 9. Probability and Markov chains 10. Real inner products and least square 11. Sabermetrics e An introduction 12. Sabermetrics e A module Appendix: A word on technology Answers and hints to selected problems

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Book SynopsisTable of ContentsPart I: Introduction and Descriptive Statistics 1. Introduction: Defining the Role of Statistics in Business 2. Data Structures: Classifying the Various Types of Data Sets 3. Histograms: Looking at the Distribution of Data 4. Landmark Summaries: Interpreting Typical Values and Percentiles 5. Variability: Dealing with Diversity Part II: Probability 6. Probability: Understanding Random Situations 7. Random Variables: Working with Uncertain Numbers Part III: Statistical Inference 8. Random Sampling: Planning Ahead for Data Gathering 9. Confidence Intervals: Admitting That Estimates Are Not Exact 10. Hypothesis Testing: Deciding Between Reality and Coincidence Part IV: Regression and Time Series 11. Correlation and Regression: Measuring and Predicting Relationships 12. Multiple Regression: Predicting One Variable From Several Others 13. Report Writing: Communicating the Results of a Multiple Regression 14. Time Series: Understanding Changes Over Time Part V: Methods and Applications 15. ANOVA: Testing for Differences Among Many Samples and Much More 16. Recent Developments 17. Chi-Squared Analysis: Testing for Patterns in Qualitative Data 18. Quality Control: Recognizing and Managing Variation 19. Statistical (Machine) Learning: Using Complex Models With Large Data Sets

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Book SynopsisTable of Contents1. Introduction 2. A Foundation for Robust Methods 3. Estimating Measures of Location and Scale 4. Confidence Intervals in the One-Sample Case 5. Comparing Two Groups 6. Some Multivariate Methods 7. One-Way and Higher Designs for Independent Groups 8. Comparing Multiple Dependent Groups 9. Correlation and Tests of Independence 10. Robust Regression 11. More Regression Methods 12. ANCOVA

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Book SynopsisTrade Review"Discrete Mathematics is adequately written and well-documented.... This book presents the material on the topic in a cogently coherent manner thereby serving and justifying the purpose of writing books such as this one. The classroom-tested pedagogy and its 400 examples speak a lot about the kind and amount of sweat that must have gone into it." --zbMATH OpenTable of ContentsPart I: Logic 1. Propositional Logic 2. Predicate Logic Part II: Set Theory and Related Topics 3. Sets 4. Matrices 5. Relations 6. Functions 7. Boolean Algebra Part III: Proof Methods 8. Sequences 9. Recursion 10. Induction 11. General Proof Methods Part IV: Number Theory and Applications 12. Elementary Number Theory 13. Cryptography Part V: Probability 14. Counting Methods 15. Discrete Probability 16. Discrete Random Variables Part VI: Graph Theory 17. Graphs 18. Trees 19. Network Models Part VII: Algorithms and Finite State Machines 20. Algorithms

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Book SynopsisTable of Contents1. An appreciation of baseball and its mathematics 2. Is baseball still the national pastime? 3. Baseball before steroids 4. Bill James and the genesis of sabermetrics 5. Rattling the sabermetrics 6. The annihilation of records: Where have you gone, Babe Ruth? 7. Steroids, etc. 8. Scandal scarred: A discussion of our national pastime’s controversial history 9. The last inning 10. Epilogue: Where have we been? Where do we go from here? A final word from the editor

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Book SynopsisTrade Review"The authors give a clear and logically correct exposition of the foundations of linear algebra and rightly determinate the balance between the computational parts and the more theoretical parts." --K.Burian, zbMATH Open "A 35-page appendix gives brief descriptions of commands needed when using computational tools such as Derive, Maple, MATLAB, Mathematica and various graphing calculators." --J.D.Dixon, zbMATH OpenTable of Contents1. Vectors and Matrices 2. Systems of Linear Equations 3. Determinants and Eigenvalues 4. Finite Dimensional Vector Spaces 5. Linear Transformations 6. Orthogonality 7. Complex Vector Spaces and General Inner Products 8. Additional Applications 9. Numerical Methods Appendices A: Miscellaneous Proofs B: Functions C: Complex Numbers D: Elementary Matrices E: Answers to Selected Exercies

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Book SynopsisTable of Contents1. Data and statistics 2. Probability and sampling distributions 3. Principles of inference 4. Inferences on a single population 5. Inferences for two populations 6. Inferences for two or more means 7. Linear regression 8. Multiple regression 9. Linear models 10. Factorial experiments 11. Design of experiments 12. Categorical data 13. Generalized linear models 14. Nonparametric methods

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Book SynopsisTrade Review"Overall, the reviewer considers this text to offer a good and useful coverage of advanced mathematics for engineers. It gives useful and succinct coverage of the topics included." --IEEE PulseTable of Contents1. Prologue 2. Ordinary Differential Equations 3. Laplace and Fourier Transform Methods 4. Matrices and Linear Systems of Equations 5. Analytical Methods for Solving Partial Differential Equations 6.Difference Numerical Methods for Differential Equations 7. Finite Element Technique 8. Treatment of Experimental Results 9. Numerical Analysis 10. Introduction to Complex Analysis 11. Nondimensionalisation 12. Nonlinear Differential Equations 13. Integral Equations 14. Calculus of Variations

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Book SynopsisAbout our author Bob Blitzer is a native of Manhattan and received a Bachelor of Arts degree with dual majors in mathematics and psychology (minor: English literature) from the City College of New York. His unusual combination of academic interests led him toward a Master of Arts in mathematics from the University of Miami and a doctorate in behavioral sciences from Nova University. Bob's love for teaching mathematics was nourished for nearly 30 years at Miami Dade College, where he received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College and an endowed chair based on excellence in the classroom. In addition to Thinking Mathematically, Bob has written textbooks covering developmental mathematics, algebra & trigonometry, trigonometry, college algebra, and precalculus, all published by Pearson. When not secluded in his Northern California writer's cabin, Bob can be found hikinTable of ContentsTable of Contents (NOTE: Each chapter concludes with a Chapter Summary, Review, and Test, and a comprehensive Chapter Test.) Problem Solving and Critical Thinking 1.1 Inductive and Deductive Reasoning 1.2 Estimation, Graphs, and Mathematical Models 1.3 Problem Solving Set Theory 2.1 Basic Set Concepts 2.2 Subsets 2.3 Venn Diagrams and Set Operations 2.4 Set Operations and Venn Diagrams with Three Sets 2.5 Survey Problems Logic 3.1 Statements, Negations, and Quantified Statements 3.2 Compound Statements and Connectives 3.3 Truth Tables for Negation, Conjunction, and Disjunction 3.4 Truth Tables for the Conditional and the Biconditional 3.5 Equivalent Statements and Variations of Conditional Statements 3.6 Negations of Conditional Statements and De Morgan’s Laws 3.7 Arguments and Truth Tables 3.8 Arguments and Euler Diagrams Number Representation and Calculation 4.1 Our Hindu-Arabic System and Early Positional Systems 4.2 Number Bases in Positional Systems 4.3 Computation in Positional Systems 4.4 Looking Back at Early Numeration Systems Number Theory and the Real Number System 5.1 Number Theory: Prime and Composite Numbers 5.2 The Integers; Order of Operations 5.3 The Rational Numbers 5.4 The Irrational Numbers 5.5 Real Numbers and Their Properties; Clock Addition 5.6 Exponents and Scientific Notation 5.7 Arithmetic and Geometric Sequences Algebra: Equations and Inequalities 6.1 Algebraic Expressions and Formulas 6.2 Linear Equations in One Variable and Proportions 6.3 Applications of Linear Equations 6.4 Linear Inequalities in One Variable 6.5 Quadratic Equations Algebra: Graphs, Functions, and Linear Systems 7.1 Graphing and Functions 7.2 Linear Functions and Their Graphs 7.3 Systems of Linear Equations in Two Variables 7.4 Linear Inequalities in Two Variables 7.5 Linear Programming 7.6 Modeling Data: Exponential, Logarithmic, and Quadratic Functions Personal Finance 8.1 Percent, Sales Tax, and Discounts 8.2 Income Tax 8.3 Simple Interest 8.4 Compound Interest 8.5 Annuities, Methods of Saving, and Investments 8.6 Cars 8.7 The Cost of Home Ownership 8.8 Credit Cards Measurement 9.1 Measuring Length; The Metric System 9.2 Measuring Area and Volume 9.3 Measuring Weight and Temperature Geometry 10.1 Points, Lines, Planes, and Angles 10.2 Triangles 10.3 Polygons, Perimeter, and Tessellations 10.4 Area and Circumference 10.5 Volume and Surface Area 10.6 Right Triangle Trigonometry 10.7 Beyond Euclidean Geometry Counting Methods and Probability Theory 11.1 The Fundamental Counting Principle 11.2 Permutations 11.3 Combinations 11.4 Fundamentals of Probability 11.5 Probability with the Fundamental Counting Principle, Permutations, and Combinations 11.6 Events Involving Not and Or; Odds 11.7 Events Involving And; Conditional Probability 11.8 Expected Value Statistics 12.1 Sampling, Frequency Distributions, and Graphs 12.2 Measures of Central Tendency 12.3 Measures of Dispersion 12.4 The Normal Distribution 12.5 Problem Solving with the Normal Distribution 12.6 Scatter Plots, Correlation, and Regression Lines Voting and Apportionment 13.1 Voting Methods 13.2 Flaws of Voting Methods 13.3 Apportionment Methods 13.4 Flaws of Apportionment Methods Graph Theory 14.1 Graphs, Paths, and Circuits 14.2 Euler Paths and Euler Circuits 14.3 Hamilton Paths and Hamilton Circuits 14.4 Trees Answers to Selected Exercises Credits Subject Index

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Book SynopsisTable of Contents1. Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions Reviewing Basic Concepts (Sections 1.1 - 1.2) 1.3 Linear Functions 1.4 Equations of Lines and Linear Models Reviewing Basic Concepts (Sections 1.3 - 1.4) 1.5 Linear Equations and Inequalities Unifying Linear Functions 1.6 Applications of Linear Functions Reviewing Basic Concepts (Sections 1.5 - 1.6) Summary Review Exercises Test 2. Analysis of Graphs of Functions 2.1 Graphs of Basic Functions and Relations; Symmetry 2.2 Vertical and Horizontal Shifts of Graphs 2.3 Stretching, Shrinking, and Reflecting Graphs Reviewing Basic Concepts (Sections 2.1 - 2.3) 2.4 Absolute Value Functions Unifying Absolute Value Functions 2.5 Piecewise-Defined Functions 2.6 Operations and Composition Reviewing Basic Concepts (Sections 2.4 - 2.6) Summary Review Exercises Test 3. Quadratic Functions 3.1 Complex Numbers 3.2 Quadratic Functions and Graphs Reviewing Basic Concepts (Sections 3.1 - 3.2) 3.3 Quadratic Equations and Inequalities Unifying Quadratic Functions 3.4 Applications of Quadratic Functions and Models Reviewing Basic Concepts (Sections 3.3 - 3.4) Summary Review Exercises Test 4. Polynomial Functions of Higher Degree 4.1 Graphs of Polynomial Functions 4.2 Topics in the Theory of Polynomial Functions (I) Reviewing Basic Concepts (Sections 4.1 - 4.2) 4.3 Topics in the Theory of Polynomial Functions (II) 4.4 Polynomial Equations, Inequalities, Applications, and Models Reviewing Basic Concepts (Sections 4.3 - 4.4) Unifying Polynomial Functions Summary Review Exercises Test 5. Rational, Power, and Root Functions 5.1 Rational Functions and Graphs (I) 5.2 Rational Functions and Graphs (II) 5.3 Rational Equations, Inequalities, Models, and Applications Reviewing Basic Concepts (Sections 5.1 - 5.3) 5.4 Functions Defined by Powers and Roots 5.5 Equations, Inequalities, and Applications Involving Root Functions Reviewing Basic Concepts (Sections 5.4 - 5.5) Unifying Root Functions Summary Review Exercises Test 6. Inverse, Exponential, and Logarithmic Functions 6.1 Inverse Functions 6.2 Exponential Functions Unifying Exponential Functions 6.3 Logarithms and Their Properties Reviewing Basic Concepts (Sections 6.1 - 6.3) 6.4 Logarithmic Functions 6.5 Exponential and Logarithmic Equations and Inequalities Unifying Logarithmic Functions 6.6 Further Applications and Modeling with Exponential and Logarithmic Functions Reviewing Basic Concepts (Sections 6.4 - 6.6) Summary Exercises on Functions: Domains, Defining Equations, and Composition Summary Review Exercises Test 7. Systems and Matrices 7.1 Systems of Equations 7.2 Solution of Linear Systems in Three Variables 7.3 Solution of Linear Systems by Row Transformations Reviewing Basic Concepts (Sections 7.1 - 7.3) 7.4 Matrix Properties and Operations 7.5 Determinants and Cramer's Rule 7.6 Solution of Linear Systems by Matrix Inverses Reviewing Basic Concepts (Sections 7.4 - 7.6) 7.7 Systems of Inequalities and Linear Programming 7.8 Partial Fractions Reviewing Basic Concepts (Sections 7.7 - 7.8) Summary Review Exercises Test 8. Conic Sections, Nonlinear Systems, and Parametric Equations 8.1 Circles Revisited and Parabolas 8.2 Ellipses and Hyperbolas Reviewing Basic Concepts (Sections 8.1 - 8.2) 8.3 The Conic Sections and Nonlinear Systems 8.4 Introduction to Parametric Equations Reviewing Basic Concepts (Sections 8.3 - 8.4) Summary Review Exercises Test 9. Trigonometric Functions and Applications 9.1 Angles, Arcs, and Their Measures 9.2 Trigonometric Functions and Fundamental Identities 9.3 Right Triangles and Evaluating Trigonometric Functions 9.4 Applications of Right Triangles 9.5 The Circular Functions 9.6 Graphs of the Sine and Cosine Functions 9.7 Graphs of the Other Circular Functions 9.8 Harmonic Motion Summary Review Exercises Test 10. Trigonometric Identities and Equations 10.1 Trigonometric Identities 10.2 Sum and Difference Identities 10.3 Further Identities 10.4 The Inverse Circular Functions 10.5 Trigonometric Equations and Inequalities (I) 10.6 Trigonometric Equations and Inequalities (II) Unifying Trigonometric Functions Summary Review Exercises Test 11. Applications of Trigonometry and Vectors 11.1 The Law of Sines 11.2 The Law of Cosines and Area Formulas 11.3 Vectors and Their Applications 11.4 Trigonometric (Polar) Form of Complex Numbers 11.5 Powers and Roots of Complex Numbers 11.6 Polar Equations and Graphs 11.7 More Parametric Equations Summary Review Exercises Test 12. Further Topics in Algebra 12.1 Sequences and Series 12.2 Arithmetic Sequences and Series 12.3 Geometric Sequences and Series Reviewing Basic Concepts (Sections 12.1 - 12.3) 12.4 Counting Theory 12.5 The Binomial Theorem Reviewing Basic Concepts (Sections 12.4 -12.5) 12.6 Mathematical Induction 12.7 Probability Reviewing Basic Concepts (Sections 12.6 - 12.7) Summary Review Exercises Test R. Review: Basic Algebraic Concepts R.1 Review of Sets R.2 Review of Exponents and Polynomials R.3 Review of Factoring R.4 Review of Rational Expressions R.5 Review of Negative and Rational Exponents R.6 Review of Radicals Test Appendices A: Geometry Formulas B: Vectors in Space C: Polar Form of Conic Sections D: Rotation of Axes Instructor's Answers Answers to Selected Exercises (Note: In the AIE, Instructor's Answers replaces Answers to Selected Exercises.) Index

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Book SynopsisTable of ContentsTable of Contents Review R.1 Real Numbers R.2 Algebra Essentials R.3 Geometry Essentials R.4 Polynomials R.5 Factoring Polynomials R.6 Synthetic Division R.7 Rational Expressions R.8 nth Roots; Rational Exponents Equations and Inequalities 1.1 Linear Equations 1.2 Quadratic Equations 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations 1.5 Solving Inequalities 1.6 Equations and Inequalities Involving Absolute Value 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Chapter 1 Review, Test, and Projects Graphs 2.1 The Distance and Midpoint Formulas 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 2.3 Lines 2.4 Circles 2.5 Variation Chapter 2 Review, Test, and Projects Functions and Their Graphs 3.1 Functions 3.2 The Graph of a Function 3.3 Properties of Functions 3.4 Library of Functions; Piecewise-defined Functions 3.5 Graphing Techniques: Transformations 3.6 Mathematical Models: Building Functions Chapter 3 Review, Test, and Projects Linear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models 4.2 Building Linear Models from Data 4.3 Quadratic Functions and Their Properties 4.4 Build Quadratic Models from Verbal Descriptions and from Data 4.5 Inequalities Involving Quadratic Functions Chapter 4 Review, Test, and Projects Polynomial and Rational Functions 5.1 Polynomial Functions 5.2 Graphing Polynomials Functions; Models 5.3 Properties of Rational Functions 5.4 The Graph of a Rational Function 5.5 Polynomial and Rational Inequalities 5.6 The Real Zeros of a Polynomial Function Chapter 5 Review, Test, and Projects Exponential and Logarithmic Functions 6.1 Composite Functions 6.2 One-to-One Functions; Inverse Functions 6.3 Exponential Functions 6.4 Logarithmic Functions 6.5 Properties of Logarithms 6.6 Logarithmic and Exponential Equations 6.7 Financial Models 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 6.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter 6 Review, Test, and Projects Trigonometric Functions 7.1 Angles, Arc, Length, and Circular Motion 7.2 Right Triangle Trigonometry 7.3 Computing the Values of Trigonometric Functions of Acute Angles 7.4 Trigonometric Functions of Any Angle 7.5 Unit Circle Approach; Properties of the Trigonometric Functions 7.6 Graphs of the Sine and Cosine Functions 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 7.8 Phase Shift; Sinusoidal Curve Fitting Chapter 7 Review, Test, and Projects Analytic Trigonometry 8.1 The Inverse Sine, Cosine, and Tangent Functions 8.2 The Inverse Trigonometric Functions (Continued) 8.3 Trigonometric Equations 8.4 Trigonometric Identities 8.5 Sum and Difference Formulas 8.6 Double-angle and Half-angle Formulas 8.7 Product-to-Sum and Sum-to-Product Formulas Chapter 8 Review, Test, and Projects Applications of Trigonometric Functions 9.1 Applications Involving Right Triangles 9.2 The Law of Sines 9.3 The Law of Cosines 9.4 Area of a Triangle 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter 9 Review, Test, and Projects Polar Coordinates; Vectors 10.1 Polar Coordinates 10.2 Polar Equations and Graphs 10.3 The Complex Plane; De Moivre’s Theorem 10.4 Vectors 10.5 The Dot Product Chapter 10 Review, Test, and Projects Analytic Geometry 11.1 Conics 11.2 The Parabola 11.3 The Ellipse 11.4 The Hyperbola 11.5 Rotation of Axes; General Form of a Conic 11.6 Polar Equations of Conics 11.7 Plane Curves and Parametric Equations Chapter 11 Review, Test, and Projects Systems of Equations and Inequalities 12.1 Systems of Linear Equations: Substitution and Elimination 12.2 Systems of Linear Equations: Matrices 12.3 Systems of Linear Equations: Determinants 12.4 Matrix Algebra 12.5 Partial Fraction Decomposition 12.6 Systems of Nonlinear Equations 12.7 Systems of Inequalities 12.8 Linear Programming Chapter 12 Review, Test, and Projects Sequences; Induction; the Binomial Theorem 13.1 Sequences 13.2 Arithmetic Sequences 13.3 Geometric Sequences; Geometric Series 13.4 Mathematical Induction 13.5 The Binomial Theorem Chapter 13 Review, Test, and Projects Counting and Probability 14.1 Counting 14.2 Permutations and Combinations 14.3 Probability Chapter 14 Review, Test, and Projects Appendix: Graphing Utilities A.1 The Viewing Rectangle A.2 Using a Graphing Utility to Graph Equations A.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry A.4 Using a Graphing Utility to Solve Equations A.5 Square Screens A.6 Using a Graphing Utility to Graph Inequalities A.7 Using a Graphing Utility to Solve Systems of Linear Equations A.8 Using a Graphing Utility to Graph a Polar Equation A.9 Using a Graphing Utility to Graph Parametric Equations Answers Credits Index

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Book SynopsisTable of ContentsPreface Prerequisite Skills Diagnostic Test R. 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 Exponential and Logarithmic Functions R.7 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 and Difference Quotients 1.5 Leibniz Notation and 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. Exponential and Logarithmic Functions 2.1 Exponential and Logarithmic Functions of the Natural Base, e 2.2 Derivatives of Exponential (Base-e) Functions 2.3 Derivatives of Natural Logarithmic Functions 2.4 Applications: Uninhibited and Limited Growth Models 2.5 Applications: Exponential Decay 2.6 The Derivatives of ax and logax Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: The Business of Motion Picture Revenue and DVD Release 3. Applications of Differentiation 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs 3.3 Graph Sketching: Asymptotes and Rational Functions 3.4 Optimization: Finding Absolute Maximum and Minimum Values 3.5 Optimization: Business, Economics, and General Applications 3.6 Marginals, Differentials, and Linearization 3.7 Elasticity of Demand 3.8 Implicit Differentiation and Logarithmic Differentiation 3.9 Related Rates Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Maximum Sustainable Harvest 4. Integration 4.1 Antidifferentiation 4.2 Antiderivatives as Areas 4.3 Area and Definite Integrals 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average 4.5 Integration Techniques: Substitution 4.6 Integration Techniques: Integration by Parts 4.7 Numerical Integration Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Business and Economics: Distribution of Wealth 5. Applications of Integration 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss 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: Lagrange Multipliers and the Extreme-Value Theorem 6.6 Double Integrals Chapter Summary Chapter Review Exercises Chapter Test Extended Technology Application: Minimizing Employees’ Travel Time in a Building Cumulative Review Appendices: A: Review of Basic Algebra B: Indeterminate Forms and l’Hôpital’s Rule C: Regression and Microsoft Excel D: Areas for a Standard Normal Distribution E: Using Tables of Integration Formulas Answers Index of Applications Index

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Book SynopsisAbout our authors Michael Sullivan, III has training in mathematics, statistics and economics, with a varied teaching background that includes 27 years of instruction in both high school- and college-level mathematics. He is currently a full-time professor of mathematics at Joliet Junior College. Michael has numerous textbooks in publication, including an Introductory Statistics series and a Precalculus series which he writes with his father, Michael Sullivan. Michael believes that his experiences writing texts for college-level math and statistics courses give him a unique perspective on where students are headed once they leave the developmental mathematics tract. This experience is reflected in the philosophy and presentation of his developmental text series. When not in the classroom or writing, Michael enjoys spending time with his 3 children, Michael, Kevin and Marissa, and playing golf. Now that his 2 sons are getting older, he has the opportuTable of ContentsTable of Contents I: GETTING THE INFORMATION YOU NEED Data Collection 1.1 Introduction to the Practice of Statistics 1.2 Observational Studies versus Designed Experiments 1.3 Simple Random Sampling 1.4 Other Effective Sampling Methods 1.5 Bias in Sampling 1.6 The Design of Experiments Chapter Review Chapter Test Making an Informed Decision: What College Should I Attend? Case Study: Chrysalises for Cash II: DESCRIPTIVE STATISTICS Organizing and Summarizing Data 2.1 Organizing Qualitative Data 2.2 Organizing Quantitative Data: The Popular Displays 2.3 Additional Displays of Quantitative Data 2.4 Graphical Misrepresentations of Data Chapter Review Chapter Test Making an Informed Decision: Tables or Graphs? Case Study: The Day the Sky Roared Numerically Summarizing Data 3.1 Measures of Central Tendency 3.2 Measures of Dispersion 3.3 Measures of Central Tendency and Dispersion from Grouped Data 3.4 Measures of Position 3.5 The Five-Number Summary and Boxplots Chapter Review Chapter Test Making an Informed Decision: What Car Should I Buy? Case Study: Who Was “A Mourner”? Describing the Relation Between Two Variables 4.1 Scatter Diagrams and Correlation 4.2 Least-Squares Regression 4.3 Diagnostics on the Least-Squares Regression Line 4.4 Contingency Tables and Association Chapter Review Chapter Test Making an Informed Decision: Relationships Among Variables on a World Scale Case Study: Thomas Malthus, Population, and Subsistence III: PROBABILITY AND PROBABILITY DISTRIBUTIONS Probability 5.1 Probability Rules 5.2 The Addition Rule and Complements 5.3 Independence and the Multiplication Rule 5.4 Conditional Probability and the General Multiplication Rule 5.5 Counting Techniques 5.6 Simulation 5.7 Putting It Together: Which Method Do I Use? Chapter Review Chapter Test Making an Informed Decision: What Are the Effects of Drinking and Driving? Case Study: The Case of the Body in the Bag Discrete Probability Distributions 6.1 Discrete Random Variables 6.2 The Binomial Probability Distribution 6.3 The Poisson Probability Distribution Chapter Review Chapter Test Making an Informed Decision: Should We Convict? Case Study: The Voyage of the St. Andrew The Normal Probability Distribution 7.1 Properties of the Normal Distribution 7.2 Applications of the Normal Distribution 7.3 Assessing Normality 7.4 The Normal Approximation to the Binomial Probability Distribution Chapter Review Chapter Test Making an Informed Decision: What Stock Do I Pick? Case Study: A Tale of Blood, Chemistry, and Health IV: INFERENCE – FROM SAMPLES TO POPULATION Sampling Distributions 8.1 Distribution of the Sample Mean 8.2 Distribution of the Sample Proportion Chapter Review Chapter Test Making an Informed Decision: How Would You Break Down Your Day? Case Study: Sampling Distribution of the Median Estimating the Value of a Parameter Using Confidence Intervals 9.1 Estimating a Population Proportion 9.2 Estimating a Population Mean 9.3 Putting It Together: Which Procedure Do I Use? 9.4 Estimating with Bootstrapping Chapter Review Chapter Test Making an Informed Decision: How Much Should I Spend for this House? Case Study: When Model Requirements Fail Hypothesis Tests Regarding a Parameter 10.1 The Language of Hypothesis Testing 10.2A Hypothesis Tests on a Population Proportion with Simulation 10.2B Hypothesis Tests on a Population Proportion Using the Normal Model 10.3A Using Simulation/Bootstrapping in Hypothesis Tests for a Population Mean 10.3B Hypothesis Tests for a Population Mean 10.4 Putting It Together: Which Procedure Do I Use? Chapter Review Chapter Test Making an Informed Decision: Selecting a Mutual Fund Case Study: How Old Is Stonehenge? Inference on Two Samples 11.1A Using Randomization Techniques to Compare Two Proportions 11.1 Inference about Two Population Proportions: Independent Samples 11.2A Using Bootstrapping to Conduct Inference on Two Dependent Means 11.2 Inference about Two Population Means: Dependent Samples 11.3A Using Randomization Techniques to Compare Two Independent Means 11.3 Inference about Two Population Means: Independent Samples 11.4 Putting It Together: Which Procedure Do I Use? Chapter Review Chapter Test Making an Informed Decision: Which Car Should I Buy? Case Study: Control in the Design of Experiment Inference on Categorical Data 12.1 Goodness-of-Fit Test 12.2 Tests for Independence and the Homogeneity of Proportions 12.3 Inference about Two Population Proportions: Dependent Samples Chapter Review Chapter Test Making an Informed Decision: What Are the Benefits of College? Case Study: Feeling Lucky? Well, Are You? Comparing Three or More Means 13.1 Comparing Three or More Means: One-Way Analysis of Variance 13.2 Post-Hoc Tests on One-Way Analysis of Variance Chapter Review Chapter Test Making an Informed Decision: Where Should I Invest? Case Study: Hat Size and Intelligence Inference of the Least-Squares Regression Model 14.1A Using Randomization Techniques on the Slope of the Least-Squares Regression Line 14.1 Testing the Significance of the Least-Squares Regression Model 14.2 Confidence and Prediction Intervals Chapter Review Chapter Test Making an Informed Decision: Buying a Home Case Study: Housing Boom Appendix A: Tables Appendix B: Lines Appendix C: Additional Topics C.1 The Normal Approximation to the Binomial Probability Distribution C.2 Estimating a Population Standard Deviation C.3 Hypothesis Tests for a Population Standard Deviation

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Book SynopsisRobert Adams is an Emeritus Professor in the Mathematics Department at the University of British Columbia. He first joined UBC in 1966 after completing a Ph.D. in Mathematics at the University of Toronto. With a keen interest in computers, mathematical typesetting, and illustration, Professor Adams became the first Canadian author in 1984 to typeset his own textbooks using TeX on a personal computer. Christopher Essex is a Professor in the Department of Applied Mathematics at the University of Western Ontario, an award-winning teacher and author. Dr. Essex did pioneering work on the thermodynamics of photon and neutrino radiation.

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