### Math 425 Prerequisites

The following background material from Math 240 will be mildly
assumed -- although it will be reviewed as needed:
- Basic linear algebra including diagonalizing matrices, symmetric
matrices and positive definite matrices

- Solving standard ordinary differential equations:

u' = cu, and au'' + bu' + cu = 0,
where a, b, c are constants.

Separation of variables for u' = f(x)g(u),

A first order linear equation: u' + a(x)u = f(x)

A first order system: U' + AU = F(x), where A is a 2 × 2
constant matrix.

- Linear Algebra: matrix computations, inner product, orthogonality,
cross product, eigenvalues and eigenvectors.

- Fourier series: expansion in orthogonal functions

- Vector calculus: curl, divergence, line integrals, surface
integrals, divergence theorem, Stokes' theorem

One way to review these is to solve the appropriate problems in old
Final Exams from
Math 240