Boyce`s Elementary Differential Equations and Boundary Value Problems (12版)

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書名：Boyce`s Elementary Differential Equations and Boundary Value Problems 12/e 作者：Boyce 裝訂：平裝 出版社：John Wiley 出版日期：2022/08/00 ISBN：9781119820512 目錄 TABLE OF CONTENTS  1 Introduction      2 First-Order Differential Equations      3 Second-Order Linear Differential Equations      4 Higher-Order Linear Differential Equations      5 Series Solutions of First-Order and Second-Order Linear Equations      6 Systems of First-Order Linear Equations      7 The Laplace Transform      8 Numerical Methods of Solving First Order Equations  9 Nonlinear Differential Equations and Stability      10 Partial Differential Equations and Fourier Series      11 Boundary Value Problems and Sturm-Liouville Theory      Web Appendix  Special Functions: On Legendre Polynomials and Functions     ANSWERS TO PROBLEMS   INDEX 

Principles of Mathematical Analysis 3/e 2023 Edition (3版)

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Principles of Mathematical Analysis 3/e 2023 Edition 作者：Walter Rudin ISBN：9786269708116 版次：3 年份：2023 出版商：McGraw-Hill 頁數/規格：342頁/平裝單色 Description This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics. NEW to This Edition The material on functions of several variables in Chapter 9 is significantly rewritten, with many details filled in, and with more examples and more motivation. The proof of the inverse function theorem is simplified by means of the fixed point theorem about contraction mappings. Differential forms are discussed in much greater detail. Several applications of Stokes' theorem are included. The Riemann-Stieltjes integral in Chapter 6 has been trimmed a bit. A short do-it-yourself section on the gamma function has been added to Chapter 8. There is a large number of new exercises throughout the book, most of them with fairly detailed hints. Several references to articles appearing in the American Mathematical Monthly and in Mathematics Magazine are included for students to develop the habit of looking into the journal literature. 目錄 Table of Contents Chapter 1: The Real and Complex Number Systems  Chapter 2: Basic Topology  Chapter 3: Numerical Sequences and Series  Chapter 4: Continuity  Chapter 5: Differentiation  Chapter 6: The Riemann-Stieltjes Integral  Chapter 7: Sequences and Series of Functions  Chapter 8: Some Special Functions  Chapter 9: Functions of Several Variables  Chapter 10: Integration of Differential Forms  Chapter 11: The Lebesgue Theory

Linear Algebra:A First Course With Applications to Differential Equations

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書名：Linear Algebra:A First Course With Applications to Differential Equations 作者：Tom M. Apostol 出版社：John Wiley ISBN：9780470067833

Princeton Lectures in Analysis III Real Analysis Measure Theory,Integration ,& Hilbert Spaces (1版)

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書名：Real Analysis: Measure Theory, Integration, And Hilbert Spaces 作者：STEIN 出版社：PRINCETON 出版日期：2005/03/14 ISBN：9780691113869

PRINCETON LECTURES IN ANALYSIS I FOURIER ANALYSIS AN INTRODUCTION (1版)

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Fourier Analysis—An Introduction 系列名：Princeton Lectures in Analysis, Volume 1 ISBN13：9780691113845 替代書名：Fourier Analysis 出版社：Princeton Univ Pr 作者：Elias M. Stein; Rami Shakarchi 裝訂：精裝 規格：24.1cm*16.5cm*1.9cm (高/寬/厚) 出版日：2003/03/17 內容簡介 This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Probability, Random Variables & Stochastic Processes (4版)

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【原文書】 書名 : Probability, Random Variables & Stochastic Processes 4/E(IE) 作者 : Athanasios Papoulis, S. Unnikrishna Pillai 出版社 : McGrasHill 出版日期 : 2002/01 ISBN : 9780071226615 Synopsis The fourth edition of "Probability, Random Variables and Stochastic Processes" has been updated significantly from the previous edition, and it now includes co-author S. Unnikrishna Pillai of Polytechnic University. The book is intended for a senior/graduate level course in probability and is aimed at students in electrical engineering, math, and physics departments. The authors' approach is to develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineering interest. Approximately 1/3 of the text is new material - this material maintains the style and spirit of previous editions. In order to bridge the gap between concepts and applications, a number of additional examples have been added for further clarity, as well as several new topics. Table of contents Part 1 Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated Trials 4 The Concept of a Random Variable 5 Functions of One Random Variable 6 Two Random Variables 7 Sequences of Random Variables 8 Statistics Part 2 Stochastic Processes 9 General Concepts 10 Random Walk and Other Applications 11 Spectral Representation 12 Spectral Estimation 13 Mean Square Estimation 14 Entropy 15 Markov Chains 16 Markov Processes and Queueing Theory

Introduction to Linear Algebra 6/e (6版)

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Introduction to Linear Algebra 6/e 作者：Gilbert Strang ISBN：9786269708109 年份：2023 出版商：New Moon Education 頁數/規格：440頁/平裝單色 Description Linear algebra now rivals or surpasses calculus in importance for people working in quantitative fields of all kinds: engineers, scientists, economists and business people. Gilbert Strang has taught linear algebra at MIT for more than 50 years and the course he developed has become a model for teaching around the world. His video lectures on MIT OpenCourseWare have been viewed over ten million times and his twelve textbooks are popular with readers worldwide. This sixth edition of Professor Strang's most popular book, Introduction to Linear Algebra, introduces the ideas of independent columns and the rank and column space of a matrix early on for a more active start. Then the book moves directly to the classical topics of linear equations, fundamental subspaces, least squares, eigenvalues and singular values – in each case expressing the key idea as a matrix factorization. The final chapters of this edition treat optimization and learning from data: the most active application of linear algebra today. Everything is explained thoroughly in Professor Strang's characteristic clear style. It is sure to delight and inspire the delight and inspire the next generation of learners. Table of Contents 1 Vectors and Matrices 2 Solving Linear Equations Ax = b 3 The Four Fundamental Subspaces 4 Orthogonality 5 Determinants 6 Eigenvalues and Eigenvectors 7 The Singular Value Decomposition (SVD) 8 Linear Transformations 9 Linear Algebra in Optimization 10 Learning from Data

ELEMENTS OF DISCRETE MATHEMATICS (2版)

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書名：Elements of Discrete Mathematics 2/e 作者：LIU 出版社：McGraw-Hill 出版日期：1985/00/00 ISBN：9780071005449 內容簡介 This book presents a selection of topics from set theory, combinatorics, graph theory, and algebra which were been considered as basic and useful to students in Applied Mathematics, Computer Seience, and Engineering. It's intended to be a textbook for a course in Discrete Mathematics at the sophomore-junior level, although it can also be used in a freshman-level course since the presentation does not assume any background beyond high-school mathematics. 目錄 1. Sets and Propositions 2. Computability and Formal Languages 3. Permutations, Combinations, and Discrete Probability 4. Relations and Functions 5. Graphs and Planar Graphs 6. Trees and Cut-Sets 7. Finite State Machines 8. Analysis of Algorithms 9. Discrete Numberic Functions and Generating Functions 10. Recurrence Relations and Recursive Algorithms 11. Groups and Rings 12. Boolean Algebras

ABSTRACT ALGEBRA (3版)

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書名：ABSTRACT ALGEBRA 3/E 作者：HERSTEIN 出版社：WILEY 出版日期：1996/03/01 ISBN：9780471368793

ABSTRACT ALGEBRA: AN INTRODUCTION (3版)

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書名：ABSTRACT ALGEBRA: AN INTRODUCTION 3/E 作者：HUNGERFORD 出版社：Cengage 出版日期：2013/00/00 ISBN：9780357670873

Contemporary Abstract Algebra (11版)

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【簡介】 ●A good mixture of approximately 1900 computational and theoretical exercises appearing in each chapter that synthesizes concepts from multiple chapters ●Back-of-the-book skeleton solutions and hints to odd-numbered exercises ●Over 300 worked-out examples ranging from routine computations to the more challenging ●Links to interactive True/False questions with comments ●Links to computer exercises that utilize interactive software available on the author's website, stressing guessing and making conjectures ●Many applications from scientific and computing fields, as well as some from everyday life ●Numerous historical notes and biographies that spotlight the people and events behind the mathematics ●Motivational and humorous quotations ●Hundreds of figures, photographs, and tables Changes to the eleventh edition include new exercises, examples, biographies, and quotes, and an enrichment of the discussion portions. These changes accentuate and enhance the hallmark features that have made previous editions of the book a comprehensive, lively, and engaging introduction to the subject. While many partial solutions and sketches for the odd-numbered exercises appear in the book, an Instructor’s Solutions Manual offers solutions for all the exercises. A Student's Solution Manual has comprehensive solutions for all odd-numbered exercises, many even-numbered exercises, and numerous alternative solutions as well. 目錄 1 Introduction to Groups 2 Groups 3 Finite Groups; Subgroups 4 Cyclic Groups 5 Permutation Groups 6 Ismorphisms 7 Cosets and Lagrange's Theorem 8 External Direct Products 9 Normal Subgroups and Factor Groups 10 Group Homomorphisms 11 Fundamental Theorem of Finite Abelian Groups 12 Introduction to Rings 13 Integral Domains 14 Ideals and Factor Rings 15 Ring Homomorphisms 16 Polynomial Rings 17 Factorization of Polynomials 18 Divisibilty in Integral Domains 19 Extension Fields 20 Algebraic Extensions 21 Finite Fields 22 Geometric Constructions 23 Sylow Theorems 24 Finite Simple Groups 25 Generators and Relations 26 Symmetry Groups 27 Symmetry and Counting 28 Cayley Digraphs of Groups 29 Introduction to Algebraic Coding Theory 30 An Introduction to Galois Theory 31 Cyclotomic Extensions