# 12-267/Topic List

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

## First-order linear equations

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

## 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

Matrix exponetiation

Phase portraits

Non-homogeneous systems

## Power-series solutions

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