Part 1. Fourier series, integrals and transforms
Fourier Series
Arbitrary Period. Even and Odd Functions. Half-Range Expansions
Forced Oscillations
Approximation by Trigonometric Polynomials
Sturm–Liouville Problems. Orthogonal Functions
Orthogonal Series. Generalized Fourier Series
Fourier Integral
Fourier Cosine and Sine Transforms
Fourier Transform. Discrete and Fast Fourier Transforms
Tables of Transforms

Part 2. Partial differential equations
Basic Concepts of PDEs
Modeling: Vibrating String, Wave Equation
Solution by Separating Variables. Use of Fourier Series
D’Alembert’s Solution of the Wave Equation. Characteristics
Modeling: Heat Flow from a Body in Space. Heat Equation
Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem
Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms
Modeling: Membrane, Two-Dimensional Wave Equation
Rectangular Membrane. Double Fourier Series
Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series
Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential
Solution of PDEs by Laplace Transforms

Part 3. Preview of Numerical ODE and PDE

Part 4. Complex Analysis