12-267/Topic List

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

The brachistochrone

First-order linear equations

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

Chain law

Variational problems

Euler-Lagrange, derivation and reductions

Lagrange multipliers

Isoperimetric Inequality

Numerical methods

Evaluating local error

Higher order constant coefficient homogeneous linear ODEs

Multiple roots

Reduction of order

Method of Undetermined Coefficients

Systems of 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

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