Second Year

Course Coordinator: J Larena

Mathematics 2 comprises two semesterized courses, MAM201 and MAM202, each comprising of 65 lectures. Credit may be obtained in each course seperately. Each semester consists of a primary and secondary stream which are run concurrently at 3 and 2 lectures per week, respectively. Additionally, a problem-based course in Mathematical Programming contributes to the class record and runs throughout the academic year.



Advanced Calculus:

Partial differentiation: directional derivatives and the gradient vector; maxima and minima of surfaces; Lagrange multipliers. Multiple integrals: surface and volume integrals in general coordinate systems. Vector calculus: vector fields, line integrals, fundamental theorem of line integrals, Green’s theorem, curl and divergence, parametric curves and surfaces. (39 Lectures.)


Groups and Geometry:

Euclidean space, geometric transformations, groups (of transformations), collineations, translations, halfturns, reflections, rotations, isometries, involutions, dilatations, symmetry and groups, the cyclic and dihedral groups, finite symmetry groups, similarities, classification of isometries (and similarities). (20 lectures.)


Mathematical Programming 1:

Introduction to the MATLAB language, basic syntax, tools, programming principles. Applications taken from MAM2 modules. Course runs over two semesters. (6 lectures.)



Linear Algebra:

Linear spaces, inner products, norms. Vector spaces, spans, linear independence, basis and di-
mension. Linear transformations, change of basis, eigenvalues, diagonalization and its applications. (39 lectures.)


Ordinary Differential Equations:

First order ordinary differential equations, linear differential equations of second order, Laplace transforms, systems of equations, series solutions, Green’s functions. (26 lectures.)


Mathematical Programming 2:

Extension of the first semester module to higher level programming and applications in linear algebra, groups and geometry.


Last Modified: Fri, 23 Jan 2015 08:09:39 SAST