Advanced Engineering Mathematics, Student Solutions Manual, 10th Edition
January 2012, ©2011
PART A. ORDINARY DIFFERENTIAL EQUATIONS (ODEs) 1
Chapter 1. First-Order ODEs 1
Chapter 2. Second-Order Linear ODEs 13
Chapter 3. Higher Order Linear ODEs 36
Chapter 4. Systems of ODEs. Phase Plane. Qualitative Methods 45
Chapter 5. Series Solutions of ODEs. Special Functions 65
Chapter 6. Laplace Transforms 79
PART B. LINEAR ALGEBRA. VECTOR CALCULUS 107
Chapter 7. Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 107
Chapter 8. Linear Algebra: Matrix Eigenvalue Problems 129
Chapter 9. Vector Differential Calculus. Grad, Div, Curl 145
Chapter 10. Vector Integral Calculus. Integral Theorems 169
PART C. FOURIER ANALYSIS. PARTIAL DIFFERENTIAL EQUATIONS (PDEs) 201
Chapter 11. Fourier Analysis 201
Chapter 12. Partial Differential Equations (PDEs) 232
- 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.