Table of Contents:

PART I: ORDINARY DIFFERENTIAL EQUATIONS
1. First-Order Differential Equations.
2. Second-Order Differential Equations.
3. The Laplace Transform.
4. Eigenfunction Expansions.

Part II: PARTIAL DIFFERENTIAL EQUATIONS
5. The Heat Equation.
6. The Wave Equation.
7. Laplace’s Equation.
8. Special Functions and Applications.
9. Transform Methods of Solution.

Part III: MATRICES AND LINEAR ALGEBRA
10. Vectors and the Vector Space Rn.
11. Matrices, Determinants and Linear Systems.
12. Eigenvalues, Diagonalization and Special Matrices.

PART IV: SYSTEMS OF DIFFERENTIAL EQUATIONS
13. Systems of Linear Differential Equations.
14. Nonlinear Systems and Qualitative Analysis.

PART V: VECTOR ANALYSIS
15. Vector Differential Calculus.
16. Vector Integral Calculus.

PART VI: FOURIER ANALYSIS
17. Fourier Series.
18. Fourier Transforms.

PART VII: COMPLEX FUNCTIONS
19. Complex Numbers and Functions.
20. Integration.
21. Series Representations of Functions.
22. Singularities and the Residue Theorem.
23. Conformal Mappings.

ADVANCED ENGINEERING MATHEMATICS, 8E is written specifically for students like you, who are primarily interested in how to effectively apply mathematical techniques to solve advanced engineering problems. Numerous examples include illustrations of mathematical techniques as well as applications. A "Math in Context" feature clearly demonstrates how the mathematical concepts and methods you are learning relate to current engineering problems. The book is organized into seven distinctive parts to provide precise focus on individual mathematical ideas and methods. A student solutions manual offers detailed solutions to half of the problems in the book for your use in checking your progress as well as study and review.