The tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis and linear algebra / differential equations.

Contents

Part A Ordinary Differential Equations (ODEs)
Chapter 1 First-Order ODEs
Chapter 2 Second-Order Linear ODEs
Chapter 3 Higher Order Linear ODEs
Chapter 4 Systems of ODEs. Phase Plane. Qualitative Methods
Chapter 5 Series Solutions of ODEs. Special Functions
Chapter 6 Laplace Transforms

Part B Linear Algebra. Vector Calculus
Chapter 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
Chapter 8 Linear Algebra: Matrix Eigenvalue Problems
Chapter 9 Vector Differential Calculus. Grad, Div, Curl
Chapter 10 Vector Integral Calculus. Integral Theorems

Part C Fourier Analysis. Partial Differential Equations (PDEs)
Chapter 11 Fourier Analysis
Chapter 12 Partial Differential Equations (PDEs)
Part D Complex Analysis
Chapter 13 Complex Numbers and Functions. Complex Differentiation
Chapter 14 Complex Integration
Chapter 15 Power Series, Taylor Series
Chapter 16 Laurent Series. Residue Integration
Chapter 17 Conformal Mapping
Chapter 18 Complex Analysis and Potential Theory

Part E Numeric Analysis
Chapter 19 Numerics in General
Chapter 20 Numeric Linear Algebra
Chapter 21 Numerics for ODEs and PDEs

Part F Optimization, Graphs
Chapter 22 Unconstrained Optimization. Linear Programming
Chapter 23 Graphs. Combinatorial Optimization

Appendix 1 References
Appendix 2 Answers to Selected Problems
Appendix 3 Auxiliary Material
Appendix 4 Additional Proofs
Appendix 5 Tables