Module  Topics 
 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  GramSchmidt 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, CauchyRiemann equation

21  e^{z} , sin z, cos z, log(z) and z^{α}

22  Complex integration

23  Cauchy's integral formula

24  Residues and the residue theorem

25  Application of the residue theorem

All modules  All modules
