Vector spaces

Basis, dimension

Linear transforms

Fundamental subspaces of a matrix

Fundamental theorem of linear algebra

Properties of rank

Inner product

Gram-Schmidt algorithm

Determinant

Properties of determinants

Introduction to eigenvalues and eigenvectors

The characteristic polynomial

Cayley-Hamilton theorem

Hermitian and symmetric matrix

Introduction to Complex Numbers

Limits and Continuity

Differentiation

Cauchy-Riemann Equations and Differentiability

Analytic functions; the exponential function

Sine, Cosine and Harmonic functions

Integration and Contours

Contour Integration

Introduction to Cauchy’s Theorem

Cauchy’s Theorem for a Rectangle