Real analysis, real variables Books
Springer Verlag, Singapore Time-Fractional Differential Equations: A Theoretical Introduction
Book SynopsisThis book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs.To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.Trade Review“The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022)Table of Contents
£52.24
Springer Verlag, Singapore Fundamentals of Analysis with Applications
Book SynopsisThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.Table of Contents1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.
£40.49
Springer Verlag, Singapore Fundamentals of Analysis with Applications
Book SynopsisThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.Table of Contents1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.
£40.49
World Scientific Publishing Co Pte Ltd Problems And Solutions In Real Analysis
Book SynopsisThis unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.Table of ContentsSequences and Limits; Infinite Series; Continuous Functions; Differentiation; Integration; Improper Integrals; Series of Functions; Approximation by Polynomials; Convex Functions; Various Proof (2) = 2 / 6; Functions of Several Variables; Uniform Distribution; Rademacher Functions; Legendre Polynomials; Chebyshev Polynomials; Gamma Function; Prime Number Theorem.
£76.95
World Scientific Publishing Co Pte Ltd Problems And Solutions In Real Analysis
Book SynopsisThis unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.Table of ContentsSequences and Limits; Infinite Series; Continuous Functions; Differentiation; Integration; Improper Integrals; Series of Functions; Approximation by Polynomials; Convex Functions; Various Proof (2) = 2 / 6; Functions of Several Variables; Uniform Distribution; Rademacher Functions; Legendre Polynomials; Chebyshev Polynomials; Gamma Function; Prime Number Theorem.
£41.80
World Scientific Publishing Co Pte Ltd Problems And Solutions In Real Analysis
Book SynopsisThis second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.
£69.35
World Scientific Publishing Co Pte Ltd Problems And Solutions In Real Analysis
Book SynopsisThis second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis.
£38.00
World Scientific Publishing Co Pte Ltd Introduction To Analysis, An
Book SynopsisThe book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.
£69.35
World Scientific Publishing Co Pte Ltd Nonabsolute Integration On Measure Spaces
Book SynopsisThis book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock-Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers.It is widely acknowledged that the biggest difficulty in defining a Henstock-Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of 'intervals' in the abstract setting. In this book the author shows a creative and innovative way of defining 'intervals' in measure spaces, and prove many interesting and important results including the well-known Radon-Nikodým theorem.
£76.00
World Scientific Publishing Co Pte Ltd Henstock-kurzweil Integration On Euclidean Spaces
Book SynopsisThe Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.Table of ContentsThe One-Dimensional Henstock-Kurzweil Integral; The Multiple Henstock-Kurzweil Integral; Lebesgue Integrable Functions; Further Properties of Henstock-Kurzweil Integrable Functions; The Henstock Variational Measure; Multipliers for the Henstock-Kurzweil Integral; Some Selected Topics in Trigonometric Series; Some Applications of the Henstock-Kurzweil Integral to Double Trigonometric Series.
£94.50
World Scientific Publishing Co Pte Ltd Fractional Calculus: Models And Numerical Methods
Book SynopsisThe subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.Table of ContentsSurvey of Numerical Methods to Solve Ordinary and Partial Fractional Differential Equations; Specific and Efficient Methods to Solve Ordinary and Partial Fractional Differential Equations; Fractional Variational Principles; Continuous-Time Random Walks (CTRWs); Applications to Finance and Economics; Generalized Stirling Numbers of First and Second Kind in the Framework of Fractional Calculus.
£121.50
World Scientific Publishing Co Pte Ltd First Course In Analysis, A
Book SynopsisThis book is an introductory text on real analysis for undergraduate students. The prerequisite for this book is a solid background in freshman calculus in one variable. The intended audience of this book includes undergraduate mathematics majors and students from other disciplines who use real analysis. Since this book is aimed at students who do not have much prior experience with proofs, the pace is slower in earlier chapters than in later chapters. There are hundreds of exercises, and hints for some of them are included.Table of ContentsSets, Functions, and Real Numbers; Sequences; Series; Continuous Functions; Differentiation; Integration; Sequences and Series of Functions.
£38.00
World Scientific Publishing Co Pte Ltd Course In Analysis, A - Volume I: Introductory
Book SynopsisPart 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.Table of ContentsIntroductory Calculus: Numbers - Revision; The Absolute Value, Inequalities and Intervals; Mathematical Induction; Functions and Mappings; Functions and Mappings Continued; Derivatives; Derivatives Continued; The Derivative as a Tool to Investigate Functions; The Exponential and Logarithmic Functions; Trigonometric Functions and Their Inverses; Investigating Functions; Integrating Functions; Rules for Integration; Analysis in One Dimension: Problems with the Real Line; Sequences and their Limits; A First Encounter with Series; The Completeness of the Real Numbers; Convergence Criteria for Series, b-adic Fractions; Point Sets in Continuous Functions; Differentiation; Applications of the Derivative; Convex Functions and some Norms on n; Uniform Convergence and Interchanging Limits; The Riemann Integral; The Fundamental Theorem of Calculus; A First Encounter with Differential Equations; Improper Integrals and the GAMMA-Function; Power Series and Taylor Series; Infinite Products and the Gauss Integral; More on the GAMMA-Function; Selected Topics on Functions of a Real Variable;
£100.80
World Scientific Publishing Co Pte Ltd Discrete Fractional Calculus: Applications In
Book SynopsisThe main subject of the monograph is the fractional calculus in the discrete version. The volume is divided into three main parts. Part one contains a theoretical introduction to the classical and fractional-order discrete calculus where the fundamental role is played by the backward difference and sum. In the second part, selected applications of the discrete fractional calculus in the discrete system control theory are presented. In the discrete system identification, analysis and synthesis, one can consider integer or fractional models based on the fractional-order difference equations. The third part of the book is devoted to digital image processing.Table of ContentsDiscrete-Variable Real Functions; The n-th Order Backward Difference/Sum of the Discrete-Variable Function; Fractional-Order Backward Differ-Sum; The FOBD-S Graphical Interpretation; The FOBD/S Selected Properties; The FO Dynamic System Description; Linear FO System Analysis; The Linear FO Discrete-Time Fundamental Elements; FO Discrete-Time System Structures; Fractional Discrete-Time PID Controller; FOS Approximation Problems; Fractional Potential; FO Image Filtering and Edge Detection; Appendix A: Selected Linear Algebra Formulae and Discrete-Variable Special Functions;
£120.60
