Partial Differential Equations I
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Reviews / Votes
From the reviews:
"These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted." (SIAM Review, June 1998)
From the reviews of the second edition:
"This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. . Graduate students . will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. . an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics." (Christian Constanda, The Mathematical Association of America, June, 2011)
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Content
- Intro
- Partial Differential Equations I
- Contents
- Contents of Volumes II and III
- Preface
- 1 Basic Theory of ODE and Vector Fields
- 2 The Laplace Equation and Wave Equation
- 3 Fourier Analysis, Distributions,and Constant-Coefficient Linear PDE
- 4 Sobolev Spaces
- 5 Linear Elliptic Equations
- 6 Linear Evolution Equations
- A Outline of Functional Analysis
- B Manifolds, Vector Bundles, and Lie Groups
- Index
