Arthur Mattuck

Lecture 01: The geometrical view of y'=f(x,y): direction fields, integral curves.

Lecture 02: Euler's numerical method for y'=f(x,y) and its generalizations.

Lecture 03: Solving first-order linear ODE's; steady-state and transient solutions.

Lecture 04: First-order substitution methods: Bernouilli and homogeneous ODE's.

Lecture 06: Complex numbers and complex exponentials.

Lecture 05: First-order autonomous ODE's: qualitative methods, applications.

Lecture 19: Introduction to the Laplace transform; basic formulas.

Lecture 09: Solving second-order linear ODE's with constant coefficients: the three cases.

Lecture 13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials.

Lecture 11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians.