MAT2243

List of Topics

Week	Section	Topic	Prerequisites	SLOs
1		Notions of linear systems of equations to introduce the concepts of vector and matrices;.
2		Vector and matrix operations: Dot and cross products, matrix transpose, determinants.
3		Vector and matrix operations: Matrix addition, multiplication and inverse.
4		Cramer's rule and solutions of linear systems
5		Full rank, undetermined, and overdetermined systems. Least square solutions
6		Eigenvalues and eigenvectors. Canonical solution to linear systems of differential equations.
7		Calculus operations in vectors and matrices, i.e. how to derive a matrix with respect to a vector?
8		Optimization: Linear problems, and nonlinear problems (constrained and unconstrained)
9		Lagrange multiplier
10		Taylor series in one and multiple variables. Jacobians and Hessians, i.e. nabla and Laplace operators.
11		Principal component analysis
12		Gradient descent
13		Neural networks as nonlinear transformations
14		Implementation of a simple neural network with gradient descent