Advanced Engineering Mathematics, 10th Edition
August 2011, ©2011
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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
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
PHOTO CREDITS P1
- 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
- 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.
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