Differential and Integral Equations

• Preface ; How to use this book ; Prerequisites ; 1. Integral equations and Picard's method ; 2. Existence and uniqueness ; 3. The homogeneous linear equation and Wronskians ; 4. The non-homogeneous linear equation: Variations of parameters and Green's functions ; 5. First-order partial differential equations ; 6. Second-order partial differential equations ; 7. The diffusion and wave equations and the equation of Laplace ; 8. The Fredholm alternative ; 9. Hilbert-Schmidt theory ; 10. Iterative methods and Neumann series ; 11. The calculus of variations ; 12. The Sturm-Liouville equation ; 13. Series solutions ; 14. Transform methods ; 15. Phase-plane analysis ; Appendix: The solution of some elementary ordinary differential equations ; Bibliography ; Index

The text is a valuable source of information on classical and modern methods of applied mathematics and is warmly recommended to mathematiians and non-mathematicians both as a textbook and as an easily accessible reference on the subject