Differential and Integral Equations

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Overview


Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis.

Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.

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Product Details

  • ISBN-13: 9780199297894
  • Publisher: Oxford University Press
  • Publication date: 9/30/2006
  • Edition description: New Edition
  • Pages: 392
  • Product dimensions: 9.60 (w) x 7.40 (h) x 0.80 (d)

Table of Contents

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

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