Table of Contents

- Introduction
- Diffusion Type Problems
- Diffusion Type Problems (Parabolic Equations)
- Boundary Conditions for Diffusion Type Problems
- Derivation of the Heat Equation
- Separation of Variables
- Transforming Nonhomogeneous BCs into Homogeneous BC
- Solving More Complicated Problems by Separation of Variables
- Transforming Hard Equations into Easier ones
- Solving Nonhomogenous PDEs (Eigenfunction Expansions)
- Integral Transforms (Sine and Cosine Transforms)
- The Fourier Series and Transform
- The Fourier Transform and its Applications to PDEs
- The Laplace Transform
- Duhamel's Principle
- The Convection Term in Diffusion Problems
- The One-Dimensional Wave Equation (Hyperbolic Equation)
- The D'Alembert Solution of the Wave Equation
- More on the D'Alembert Solution
- Boundary Conditions associated with the Wave Equation
- The Finite Vibrating String (Standing Waves)
- The Vibrating Beam (Fourth-Order PDE)
- Dimensionless Problems
- Classification of PDEs (Canonical Form of the Hyperbolic Equation)
- The Wave Equation in Two and Three Dimensions (Free space)
- The Finite Fourier Transforms (Sine and Cosine Transforms)
- Superposition
- First order Equations (Methods and Characteristics)
- Nonlinear First-Order Equations (Conservation Equations)

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