12-267/Topic List

Here is a (incomplete) list of subjects covered in MAT267 this semester.

First-order linear equations

Solution techniques

The brachistochrone

Separable equations

Escape velocities

Changing source and target coordinates

Homogeneous equations

Reverse-engineering separable and exact equations

Solving exact equations with and without integration factors

Fundamental Theorem and proof

Calculus of Variations

Chain law

Euler-Lagrange, derivation (alternate) and reductions

Lagrange multipliers

Isoperimetric Inequality

Numerical methods

Examples and derivations

Evaluating local error

Higher Order Constant Coefficient Homogeneous Linear ODEs

Multiple roots

Reduction of order

Method of Undetermined Coefficients

Systems of First-Order Linear Equations

Solution techniques

Matrix exponetiation

Phase portraits

Non-homogeneous systems

Power-series solutions

Quick guide

Global existence for linear ODEs

Wronskian

Series solutions for y' = f(x,y)

Radius of convergence

Qualitative Analysis

Airy's equation

Fuch's Theorem

Regular singular points

Frobenius series and Frobenius Method

The basic oscillation theorem

Non-oscillation theorem

Sturm comparison theorem

Changing the independent variable

Amplitudes of oscillations