Lecture Notes
A Review of Linear Algebra and Ordinary Differential Equations

An Introduction to Complex Variables

Linear Algebra
1  Vectors, space, subspace, span
2  Linear independence, basis and dimension
3  Inner products
4  Orthogonal projections
5  Best approximation and orthogonal projections
6  Gram-Schmidt orthogonalization process
7  Linear Operators
8  Null space, range, column space, row space and rank
9  Square systems, determinants and eigenvalues
10  Some examples and applications
11  Hermitian and symmetric matrices
11a  The vector norm of a matrix
Ordinary Differential Equations
12  Ordinary differential equations
13  Linear systems
14  Linear inhomogeneous equations
15  Linear equations with constant coefficients
16  Scalar differential equations with constant coefficients
17  The inverse of linear operators and Green's functions
18  Eigenvalues and eigenvectors for differential operators
Complex Variables
19 The number system and complex numbers
20  Functions of a complex variable, Cauchy-Riemann equation
21  ez , sin z, cos z, log(z) and zα
22  Complex integration
23  Cauchy's integral formula
24  Residues and the residue theorem
25  Application of the residue theorem
All modules  All modules