Differential And Integral Equations

Paperback | September 3, 2006

byPeter J. Collins

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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 partialdifferential 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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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 partialdifferential equations, whilst introducing i...

Peter J. Collins is at St. Edmund Hall, University of Oxford.

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Format:PaperbackDimensions:392 pages, 9.69 × 7.44 × 0.87 inPublished:September 3, 2006Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199297894

ISBN - 13:9780199297894

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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

Editorial Reviews

`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'Yuri V. Rogovchenko, Zentralblatt MATH