Textbook

Advanced Engineering Mathematics, 10th Edition

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This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.

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Table of Contents

P A R T A Ordinary Differential Equations (ODEs) 1

CHAPTER 1 First-Order ODEs 2

CHAPTER 2 Second-Order Linear ODEs 46

CHAPTER 3 Higher Order Linear ODEs 105

CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 124

CHAPTER 5 Series Solutions of ODEs. Special Functions 167

CHAPTER 6 Laplace Transforms 203

P A R T B Linear Algebra. Vector Calculus 255

CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 256

CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 322

CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 354

CHAPTER 10 Vector Integral Calculus. Integral Theorems 413

P A R T C Fourier Analysis. Partial Differential Equations (PDEs) 473

CHAPTER 11 Fourier Analysis 474

CHAPTER 12 Partial Differential Equations (PDEs) 540

P A R T D Complex Analysis 607

CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 608

CHAPTER 14 Complex Integration 643

CHAPTER 15 Power Series, Taylor Series 671

CHAPTER 16 Laurent Series. Residue Integration 708

CHAPTER 17 Conformal Mapping 736

P A R T E Numeric Analysis 787

Software 788

CHAPTER 19 Numerics in General 790

CHAPTER 20 Numeric Linear Algebra 844

CHAPTER 21 Numerics for ODEs and PDEs 900

P A R T F Optimization, Graphs 949

CHAPTER 22 Unconstrained Optimization. Linear Programming 950

CHAPTER 23 Graphs. Combinatorial Optimization 970

CHAPTER 24 Data Analysis. Probability Theory 1011

CHAPTER 25 Mathematical Statistics 1063

APPENDIX 1 References A1

APPENDIX 2 Answers to Odd-Numbered Problems A4

APPENDIX 3 Auxiliary Material A63

APPENDIX 4 Additional Proofs A77

APPENDIX 5 Tables A97

INDEX I1

PHOTO CREDITS P1

New To This Edition

Revised Problem Sets: This edition includes an extensive revision of the problem sets, making them even more effective, useful, and up-to-date.
Chapter Introductions: These have also been rewritten to be more accessible and helpful to students.
Rewrites: Some material has been rewritten specifically to better help students draw conclusions and tackle more advanced material.
Chapter Revisions: Many of the chapters in this edition have been rewritten entirely. Some have had material added, including but not limited to:
Introduction of Euler’s Method in section 1.2
Partial Derivatives on a Surface in section 9.6
Introduction to the Heat Equation in section 12.5

Hallmark Features

Simplicity of Examples: To make the book teachable, why choose complicated examples when well-written simple ones are as instructive or even better?
Independence of Chapters: To provide flexibility in tailoring courses to special needs.
Self-Contained Presentation: Except for a few clearly marked places where a proof would exceed the level of the book and a reference is given instead.
Modern Standard Notation: To help students with other courses, modern books, and mathematical and engineering journals.