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Chapter 1. Introduction
- Section 1.1 Concept and Examples
(pages 1 - 10)
- Section 1.2. First-Order Equations. Method of Characteristics
(pages 99 - 108)
- Section 1.3. Classification of Second-Order Equations
Notes
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Chapter 2. Laplace's Equation and Poisson's Equation
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Section 2.1. Method of Separation of Variables
(pages 11 - 22)
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Section 2.2. Fundamental Solution and Green's Functions
(pages 23 - 30)
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Section 2.3. Mean-Value Theorem and Maximal Principles
(pages 31 - 41)
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Section 2.4. Variational Methods
Chapter 3. Heat Equation
- Section 3.1. Method of Separation of Variables. Eigenfunction Expansions.
(pages 42 - 51)
- Section 3.2. Fourier Transforms. Fundamental Solutions
(pages 52 - 66)
- Section 3.3. Mean-Value Theorem and Maximal Principles
(pages 67 - 75)
- Section 3.4. Gradient Flow and Variational Methods
Chapter 4. Wave Equation
- Section 4.1. Method of Separation of Variables
(pages 76 - 84)
- Section 4.2. D'Alembert's Formula. Spherical Means
(pages 85 - 93)
- Section 4.3. Method of Fourier Transforms
- Section 4.4. Energy Method. Dissipation and Dispersion
(pages 94 - 98)
Chapter 5. Some Nonlinear Equations
- Section 5.1. Nonlinear Reaction-Diffusion Equations
- Section 5.2. Hamilton-Jacobi Equations
- Section 5.3. Hyperbolic Conservation Laws
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