Partial Differential Equations I

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 Equation. - 6 Linear Evolution Equations. - A Outline of Functional Analysis. - B Manifolds, Vector Bundles, and Lie Groups. - Index.