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Title: Partial Differential Equations: Basic Theory (Texts in Applied Mathematics, 23) by Michael E. Taylor ISBN: 0-387-94654-3 Publisher: Springer Verlag Pub. Date: June, 1996 Format: Paperback Volumes: 1 List Price(USD): $59.95 |
Average Customer Rating: 4.5 (2 reviews)
Rating: 5
Summary: Complete, accurate and well-written.
Comment: The author accomplished the goal of presenting this broad and many-faceted subject in a thorough and comprehensive manner. Beginning from the fundamentals of ODE theory to the most sophisticated methods for solving important PDE's of mathematical physics, this series of three volumes comprises all what a modern analyst must know about the topic and much more.
The contents of volume 1 are: Basic theory of ODE; Laplace and wave equations; Fourier analysis, distributions, and constant-coefficient linear PDE; Sobolev spaces; linear elliptic equations; linear evolution equations. Appendices: Outline of functional analysis; manifolds, vector bundles, and Lie groups.
Originally intended for graduate students and working mathematicians, most of the material is suitable for advanced undergraduate courses. Includes excercises for each section and extensive references.
Rating: 4
Summary: ODE
Comment: Much material is included in this text, which is the first volume in a set of three and is suitable for graduate students and professionals. Chapter one details much material about ODE focusing on vector fields and much more including: Lie brackets, differential forms, geodesics, variable coefficient linear ODE, and of course, existence and uniqueness. Subsequent chapters cover Laplace's equation, Fourier Analysis and its relations to constant - coefficient linear PDE, linear Elliptic equations, Sobolev spaces, and linear evolution equations. Finally two important appendices are indcluded: One concerning functional analysis and another concerning differential geometry.
While these chapters are essential self contained the chapter on sobolev spaces is important for later volumes. Overall the writing is rigorous and demanding --- as most mathemtical texts of this level are. However, with the assistance of a good library and dilligent effort *much* can be obtained from this set of texts, which explains precisely what is currently known about the genernal theory of PDE.
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Title: Partial Differential Equations II: Qualitative Studies of Linear Equations (Applied Mathematical Sciences, Volume 116) by Michael E. Taylor ISBN: 0387946519 Publisher: Springer Verlag Pub. Date: June, 1996 List Price(USD): $79.95 |
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Title: Introduction to Smooth Manifolds by John M. Lee ISBN: 0387954481 Publisher: Springer Verlag Pub. Date: 23 September, 2002 List Price(USD): $49.95 |
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Title: Advanced Calculus : Second Edition by David V. Widder ISBN: 0486661032 Publisher: Dover Pubns Pub. Date: 01 August, 1989 List Price(USD): $17.95 |
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Title: General Relativity by Robert M. Wald ISBN: 0226870332 Publisher: University of Chicago Press Pub. Date: July, 1984 List Price(USD): $37.00 |
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Title: Partial Differential Equations III: Nonlinear Equations (Applied Mathematical Sciences (Springer-Verlag), Vol 117) by Michael E. Taylor ISBN: 0387946527 Publisher: Springer Verlag Pub. Date: June, 1996 List Price(USD): $79.95 |
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