Partial Differential Equations | An Introduction

1. Examples.- 1. Introduction.- 2. The Wave Equation.- 3. The Potential Equation.- 4. The Heat Equation.- 2. Classification into Types, Theory of Characteristics, and Normal Form.- 1. Differential Equations of the First Order.- 2. Systems of Differential Equations of the First Order.- 3. On the Necessity of Classification Into Types.- 3. Questions of Uniqueness.- 1. Elliptic and Elliptic-Parabolic Type.- 2. Parabolic Type.- 3. Hyperbolic Type.- 4. Mixed Type.- 4. Questions of Existence.- 1. Equations of Hyperbolic Type in Two Independent Variables.- 2. Boundary and Initial-Value Problems for Equations of Hyperbolic and Parabolic Type in Two Independent Variables.- 3. Equations of Elliptic Type.- 4. Weyl's Lemma for Equations of Elliptic Type.- 5. Simple Tools from Functional Analysis Applied to Questions of Existence.- 1. Auxiliary Tools.- 2. Schauder's Technique of Proof for Existence Problems in Elliptic Differential Equations.- 3. The Regular Eigenvalue Problem.- 4. Elliptic Systems of Differential Equations.- Solutions.