Differential and Integral Equations

Peter J. Collins (St Edmund Hall, University of Oxford)

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English

Oxford University Press
01 September 2006

Algebra; Differential calculus & equations; Integral calculus & equations

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'.

By: Peter J. Collins (St Edmund Hall University of Oxford)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 195mm, Spine: 26mm
Weight: 912g
ISBN: 9780198533825
ISBN 10: 0198533829
Pages: 381
Publication Date: 01 September 2006
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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

Reviews for Differential and Integral Equations

`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