Differential and Integral Equations (Paperback)
- 出版商: Oxford University
- 出版日期: 2006-08-01
- 售價: $1,150
- 貴賓價: 9.8 折 $1,127
- 語言: 英文
- 頁數: 392
- 裝訂: Paperback
- ISBN: 0199297894
- ISBN-13: 9780199297894
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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'.
Table of Contents
PrefaceHow to use this bookPrerequisites1. Integral equations and Picard's method2. Existence and uniqueness3. The homogeneous linear equation and Wronskians4. The non-homogeneous linear equation: Variations of parameters and Green's functions5. First-order partial differential equations6. Second-order partial differential equations7. The diffusion and wave equations and the equation of Laplace8. The Fredholm alternative9. Hilbert-Schmidt theory10. Iterative methods and Neumann series11. The calculus of variations12. The Sturm-Liouville equation13. Series solutions14. Transform methods15. Phase-plane analysisAppendix: The solution of some elementary ordinary differential equationsBibliographyIndex