Fourier Transformation and Sobolev Spaces: Introduction. Functions in Rn. Fourier Transformation and Distributions in Rn. Sobolev Spaces. Exercises. Notes. Pseudodifferential Symbols: Introduction. Definition and Approximation of Symbols. Oxcillatory Integrals. Operations on Symbols. Exercises. Pseudodifferential Operators: Action in S and S'. Action in Sobolev Spaces. Invariance Under a Change of Variables. Exercises. Notes. Applications: Introduction. Local Solvability of Linear Differential Operators. Wave Front Sets of Solutions of Partial Differential Equations. The Cauchy Problem for the Wave Equation. Exercises. Notes. Index of Notations. References.
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