Direction Fields and Integral Curves (MIT 18.03, Lecture 1)

Euler's Numerical Method for y'=f(x,y) and its Generalizations (MIT 18.03, Lecture 2)

First-order Linear ODEs: Steady-state and Transient Solutions (MIT 18.03, Lecture 3)

First-Order Substitution Methods: Bernoulli and Homogeneous ODEs (MIT 18.03, Lecture 4)

First-order Autonomous ODEs: Qualitative Methods and Applications (MIT 18.03 Differential Equations, Lecture 5)

Complex Numbers and Complex Exponentials (MIT 18.03, Lecture 6)

First-order Linear Differential Equations with Constant Coefficients (MIT 18.03, Lecture 7)

Lecture 8: Applications to Temperature, Mixing, RC-Circuit, Decay, and Growth Models (18.03)

Lecture 10: Complex Characteristic Roots; Undamped and Damped Oscillations (18.03)

Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians (18.03)

Lecture 12: General Theory for Inhomogeneous ODE's; Stability Criteria for Constant-coefficient ODE's (18.03)

Lecture 13: Finding Particular Solutions to Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials (18.03)

Lecture 14: Interpretation of the Exceptional Case: Resonance (18.03)

Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2π (18.03)

Lecture 16: More General Periods; Even and Odd Functions; Periodic Extension (18.03)

Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds (18.03)

Lecture 19: Introduction to the Laplace Transform; Basic Formulas (18.03)

Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's (18.03)

Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems (18.03)

Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs (18.03)