First level: Any TWO APM modules, MAT111, 103 and any TWO of MAT101, 102 112, 113 Second level: APM211, 212
Third level: FOUR of the following combinations: (a) APM301, 214 (b) APM311, 213, COS111 (c) APM312, 215 (d) APM313, 215 (e) MAT306, 211 (f) MAT307, 212
.4
...
SYLLABUS
First-level modules
APM111-S Mechanics I* Prerequisite:ONE of the following:
(a) at least 50% (D symbol) in Mathematics HIGHER GRADE at Matriculation level (b) Mathematics at Matriculation level passed prior to differentiation
(c) An equivalent examination in Mathematics (see Sc1(1)(b)(iv) in Section 6 of Part 2 of the Calendar)
(d) MAT110 (e) PHY101
Purpose: to introduce students to vectors; static equilibrium; uniformly accelerated motion; Newton's laws; work and energy; linear momentum; motion in a circle; rotational work, energy and momentum; mechanical properties of matter; vibration and waves.
APM112-T Mechanics II Prerequisite:
ONE of the following:
(a) At least 50% (D symbol) in Mathematics HIGHER GRADE at Matriculation level (b) Mathematics at Matriculation level passed prior to differentiation
(c) An equivalent examination in Mathematics (see Sc1(1)(b)(iv) in Section 6 of Part 2 of the Calendar)
(d) MAT110
Purpose: to enable students to demonstrate a basic understanding of definite integrals, line integrals and the vector product; dynamics of systems of particles and rigid bodies in particular mass centres, moments of forces, moments of inertia and angular momentum; non-inertial systems, fictitious forces, equivalence principle.
APM113-U Applied Linear Algebra* Prerequisite:
ONE of the following:
(a) At least 50% (D symbol) in Mathematics HIGHER GRADE at Matriculation level (b) Mathematics at Matriculation level passed prior to differentiation
(c) An equivalent examination in Mathematics (see Sc1(1)(b)(iv) in Section 6 of Part 2 of the Calendar)
(d) MAT110
Purpose: to enable students to master and apply the following aspects of the numerical solution of systems of linear equations: the method of least squares; linear programming (simplex method); eigenvalues, eigenvectors, diagonalisation as well as some miscellaneous applications. APM114-V Mathematical Modelling
Prerequisite: ONE of the following:
(a) At least 50% (D symbol) in Mathematics HIGHER GRADE at Matriculation level (b) Mathematics at Matriculation level passed prior to differentiation
(c) An equivalent examination in Mathematics (see Sc1(1)(b)(iv) in Section 6 of Part 2 of the Calendar)
(d) MAT110
Purpose: to enable students to demonstrate a basic understanding of solution, equilibrium points and stability of difference equations and first-order differential equations; applications to population models; harvesting strategies; epidemics; economics and other situations; simple optimisation and applications.
Second-level modules
APM211-V Differential equations*
Prerequisite: Any TWO of MAT101, 102, 112, 113
Advice: Aspects of linear algebra, as treated in MAT103, is used in this module.
Purpose: to enable students to obtain knowledge of first-order ordinary differential equations, linear differential equations of higher order, series solutions of differential equations (method of Frobenius), Laplace transform and partial differential equations (only an introduction).
APM212-W Calculus in higher dimensions
Prerequisite: Any TWO of MAT101, 102, 112, 113 and MAT111 (or 103)
Purpose: to enable students to gain a clear knowledge and understanding of vectors in n-space, functions from n-space to m-space, various types of derivatives (grad, div, curl, directional derivatives), higher-order partial derivatives, inverse and implicit functions, double integrals, triple integrals, line integrals and surface integrals, and the theorems of Green, Gauss and Stokes. APM213-X Numerical methods 1 (3 hours)*
Prerequisite: COS111, MAT111, 103 and any TWO of MAT101, 102, 112, 113
Purpose: to introduce students to numerical solutions of non-linear equations and systems of linear equations; interpolating polynomials, numerical integration and differentiation, least-squares approximation.
APM214-Y Applied dynamical systems
Prerequisites: Any three of MAT111, 101, 102, 103, 112, 113
Purpose: to enable students to master and apply fundamental aspects of discrete and continuous systems including linear systems; phase portraits: equilibrium points, stability, limit cycles; Liapunov stability; elementary control theory as well as applications to mechanics, ecology, economics and elsewhere.
APM215-3 Differential Geometry
Prerequisites: Any three of MAT111, 101, 102, 103, 112, 113
Advice: A knowledge of elementary vector algebra as presented in APM112 is assumed. Purpose: to introduce students to the following topics in the differential geometry of curves and surfaces: parametric equations of curves, arc length, tangent, principal normal and binormal lines, normal, oscillating and rectifying planes, curvature and torsion, Serret-Frenet equations, theory of surfaces: parametric equations of a surface, implicit and explicit equations of a surface, curvilinear coordinates, tangent plane, parametric transformations, first and second fundamental forms, principal curvatures, mean and Gaussian curvature, elliptic, parabolic and hyperbolic points, principal directions, lines of curvature, Rodrigues' formula, Euler's theorem, Dupin indicatrix, Christoffel relations, Gauss-Codazzi-Weingarten equations.
Third-level modules
Prerequisite: Any two APM or MAT modules on second level APM301-W Partial differential equations*
Advice: The content of APM211 (or MAT216) is assumed as known in this module.
Purpose: to introduce students to the following topics in partial differential equations; the equation of Laplace, the heat equation and the wave equation treated as typical examples of elliptic, parabolic and hyperbolic partial differential equations respectively, and methods of solution of the corresponding boundary value problems are also discussed.
APM311-Y Numerical methods 2*
Advice: The content of APM213 (or COS233) is assumed as known in this module.
Purpose: to enable students to demonstrate a basic understanding of numerical solution methods for ordinary differential equations and boundary value problems, numerical solution methods for elliptic partial differential equations, and function approximations.
APM312-3 Mechanics and the calculus of variations
Advice: The modules APM212 (or MAT215) and PHY201 contain useful background material. Purpose: to enable students to demonstrate a basic understanding of generalised coordinates, Hamilton's principle, calculus of variations and the Euler-Lagrange equations, the problem of Lagrange and the isoperimetric problem, Hamilton-Jacobi theory and Poisson brackets, Equivalent
Lagrangians, canonical transfomations and Noether's theorem and application of the variational principles in mechanics.
APM313-4 Special relativity and Riemannian geometry Advice: The content of APM215 is assumed as known in this module.
Purpose: to enable students to demonstrate a basic understanding of Einstein's special relativity theory and Maxwell's electromagnetic theory. Riemannian geometry and tensor calculus.