Second Year Courses (2013)

The course “Mathematics and Applied Mathematics 2” comprises two semesters which provide the credits MAM 201 and MAM 202.

Each semester is sub-divided into three modules, listed below.

MAM 201 (first semester):

Advanced Calculus (25 lectures, M Burton). Partial differentiation; directional derivatives and the gradient vector, maximum and minimum values, Lagrange multipliers. Multiple integrals; double and triple integrals in various coordinate systems; Vector calculus: vector fields, line integrals, fundamental theorem for line integrals, Green's theorem, curl and divergence.

Geometry* (15 lectures, D Barrett). The Euclidean plan, transformations (collineations, dilatations), groups of transformations, isometries (translations, half-turns, reflections, glide reflections), classification of isometries.

Discrete Mathematics* (15 lectures, V Murali). Review of elementary counting, multisets and multinomial theorem, the principle of inclusion and exclusion, inversion formulae.

Linear Algebra (25 lectures, AL Pinchuck). Vector spaces, subspaces, null spaces and spans, linear independence, basis and dimension, linear transformations, change of basis, eigenvalues and eigenvectors, diagonalization and applications.

(* Geometry and Discrete Mathematics run concurrently and are offered as options. Students are asked to select one of the two to complete their MAM 201 credit.)

MAM 202 (second semester):

Calculus of Variations (15 lectures, D Pollney). This course develops variational principles for solving minimization problems. We introduce the concept of a functional and the Principle of Least Action leading to the Euler-Lagrange equations determining geodesics. Geometrical symmetries determine conserved variables via Noether's theorem. The ideas are illustrated through application to classical problems in dynamics.

Differential Equations (25 lectures, JV Van Zyl). First order ordinary differential equations; linear differential equations of second order; series solutions; Laplace transforms; systems of first order ODEs.

Numerical Methods (25 lectures, M Burton). Computations with MATLAB, programming with MATLAB, applications to systems of linear equations, linear regression, interpolation, numerical differentiation, quadrature.

2013 Course Coordinator : Dr D Pollney