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Calculus, Volume 1 2/e ISBN13:9780471000051 出版社:Wiley 作者:APOSTOL 裝訂:精裝 版次:2 出版日:1991/10/00
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詳細資訊
Calculus, Volume 1 2/e ISBN13:9780471000051 出版社:Wiley 作者:APOSTOL 裝訂:精裝 版次:2 出版日:1991/10/00
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書名:Calculus Volume 2 2/e 作者:APOSTOL 出版社:John Wiley 出版日期:1969/06/20 ISBN:9780471000075 內容簡介 Volume I presents one-variable calculus with an introduction to linear algebra and volume II presents multi-variable calculus and linear algebra, with applications to differential equations and probability 目錄 PART 1 Linear Analysis. 1.Linear Spaces. 2.Linear Transformations and Matrices. 3.Determinants. 4.Eigenvalues and Eigenvectors. 5.Eigenvalues of Operators Acting on Euclidean Spaces. 6.Linear Differential Equations. 7.Systems of Differential Equations. PART 2 Nonlinear Analysis. 8.Differential Calculus of Scalar and Vector Fields. 9.Applications of the Differential Calculus. 10.Line Integrals. 11.Multiple Integrals 12.Surface Integrals PART 3 Special Topics. 13.Set Functions and Elementary Probability. 14.Calculus of Probabilities. 15.Introduction to Numerical Analysis.
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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
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This textbook is carefully designed as an early undergraduate introduction to the calculus of several real variables. The balanced coverage is devoted to limits, continuity, partial derivatives, extrema, the nabla operator, multiple integrals, line integrals, surface integrals, and the fundamental theorems of vector calculus. Engaging and accessible with detailed diagrams and copious worked examples, the presentation is well suited to students pursuing applied fields such as engineering. Multiple integration is motivated intuitively through the calculation of mass. The chapter-end problems provide both drill and challenge. Overall, the book should equip students with the knowledge and confidence needed for subsequent courses. An appendix on hints renders the book suitable for self-study. Prerequisites are limited to single-variable calculus, linear algebra, and analytic geometry. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Preliminaries: Lines, Trajectories, Surfaces, and 3D Figures Contents: Preface About the Authors Preliminaries Differential Calculus Double Integrals Triple Integrals Line Integrals Surface Integrals The Principal Theorems Appendix A: Fields in Curvilinear Coordinates Appendix B: Hints and Answers Index Readership: Undergraduate students in mathematics, science, and engineering, as well as practicing engineers.