Advanced Mathematics for Applications

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Andrea ProsperettiCambridge University PressEdition: Illustrated, 1/6/2011EAN 9780521735872, ISBN10: 0521735874Paperback, 742 pages, 24.6 x 17.3 x 3.6 cmLanguage: EnglishOriginally published in EnglishThe partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.PrefaceTo the readerList of tablesPart I. General Remarks and Basic Concepts1. The classical field equations2. Some simple preliminariesPart II. Applications3. Fourier seriesapplications4. Fourier transformapplications5. Laplace transformapplications6. Cylindrical systems7. Spherical systemsPart III. Essential Tools8. Sequences and series9. Fourier seriestheory10. The Fourier and Hankel transforms11. The Laplace transform12. The Bessel equation13. The Legendre equation14. Spherical harmonics15. Green's functionsordinary differential equations16. Green's functionspartial differential equations17. Analytic functions18. Matrices and finite-dimensional linear spacesPart IV. Some Advanced Tools19. Infinite-dimensional spaces20. Theory of distributions21. Linear operators in infinite-dimensional spacesAppendixReferencesIndex. Show more