This course gives students overviews of linear first and second order ordinary differential equations (OEDs) and linear algebra. The math skills will be applied to atmospheric sciences problems.

First order ODEs:
- responses to (complex) exponential, oscillating, delta function inputs
- integrating factor
- separable euqations

Second order ODEs:
- fundamental equation of mechanics
- forced harmonic motion
- unforced damped motion
- impulse response, exponential response
- method of undetermined coefficients
- variation of parameters

Linear algebra:
- row and column view of matrix multiplication
- independence, basis, and dimension
- four fundamental subspaces
- factorization
(i) A = LU: LU elimination
(ii) A = QR: orthogonalization (Gram-Schmidt)
(iii) S = Q??QT: eigenvalues
(iv) A = X??XT, diagonalization
(v) A = U??VT, singular value decomposition

Solving linear system:
- matrix exponential
- phase plane: source, sink, saddle