Differential Equations

From slope fields to the heat, wave and Laplace equations.

Syllabus

  1. First-Order ODEs & Dynamics

    1. What a Differential Equation Is — Slope Fields & Initial-Value Problems
    2. First-Order Methods — Separable, Linear & Exact
    3. Autonomous Equations, Equilibria & Stability

  2. Linear ODEs & Systems

    1. Second-Order Linear ODEs — The Three Cases
    2. Forcing, Undetermined Coefficients & Resonance
    3. The Laplace Transform
    4. Systems of ODEs & Phase Portraits

  3. Fourier & the Bridge to PDEs

    1. Fourier Series
    2. The Fourier Transform

  4. Partial Differential Equations

    1. Separation of Variables
    2. The Heat Equation
    3. The Wave Equation
    4. Laplace's Equation & Boundary-Value Problems
    5. Classification, Numerics & Course Capstone