Applied Mathematics modules for BEng students Toegepaste Wiskunde modules vir BIng studente 2023

Further information, including credit values and prerequisites, can be found in Part 5 and Part 11 of the university's Calendar. Verdere inligting, insluitende kredietwaardes en voorvereistes, kan in Deel 5 en Deel 11 van die universiteit se Jaarboek gevind word.

First yearEerste jaar

StaticsStatika (TWB124)
(1ste semester)
Dr de Villiers, Prof Fidder (coordinator), Mr Josias, Dr Landi, Mr Mungwe, Ms Stander

Vectors; forces; sum of forces at a point; direction cosines and direction angles; components and component vectors; scalar and vector products; moment of a force; force systems on rigid bodies; equivalent force systems; couples; line of action of the resultant; equilibrium of a rigid body; friction; centre of mass; centroid; volumes; definite integration; moment of inertia of areas. Vektore; kragte; som van kragte by 'n punt; rigtingcosinusse en rigtingshoeke; komponente en komponent-vektore; skalaar- en vektorprodukte; moment van 'n krag; kragstelsels op starre liggame; ekwivalente kragstelsels; koppels; werklyn van die resultante; ewewig van starre liggame; wrywing; massamiddelpunte; sentroïde; volumes; bepaalde integrasie; traagheidsmomente van areas.

DynamicsDinamika (TWB154)
(2ndde semester)
Dr Cloete (coordinator), Dr Coetze, Dr Roux, Prof Smit

Kinematics of a particle: continuous and erratic rectilinear motion; curvilinear motion in the following coordinate systems: Cartesian, normal-tangential, cylindrical; pulley systems and relative motion. Kinetics of a particle: equations of motion – Newton 2 in all three coordinate systems; principle of work and energy; energy conservation; power; principle of linear impulse and momentum; conservation of linear momentum; impact. Kinematika van 'n partikel: kontinue en onreëlmatige reglynige beweging; kromlynige beweging in die volgende koördinaatstelsels: Cartesies, normaal-tangent, silindries; katrolstelsels en relatiewe beweging. Kinetika van 'n partikel: bewegingsvergelykings – Newton 2 in al drie koördinaatstelsels; arbeid-energiebeginsel; energiebehoud; drywing; beginsel van lineêre impuls en momentum; lineêre momentumbehoud; impak.

Second yearTweede jaar

Dynamics of Rigid BodiesDinamika van Starre Liggame (TWB224)
(1ste semester)
Dr Coetzer, Dr Cloete, Prof Smit (coordinator)

Plane kinetics of rigid bodies; rotation and translation; absolute motion; relative motion; instantaneous centre of zero velocity. Properties of rigid bodies; definite and multiple integrals; Cartesian, polar, cylindrical and spherical coordinate systems; moments of inertia. Plane kinetics of rigid bodies; Newton's laws; energy methods. Vibrations of rigid bodies. Vlakkinematika van starre liggame; rotasie en translasie; absolute beweging; relatiewe beweging; oombliklike rotasie-as. Eienskappe van starre liggame; bepaalde en meervoudige integrasie; Cartesiese, pool-, silindriese en sferiese koördinaatstelsels; traagheidsmomente. Vlakkinetika van starre liggame; Newton se wette; energiemetodes. Vibrasies van starre liggame.

Vector Analysis Vektoranalise (TWB242)
(2ndde semester)
Dr Maritz

The straight line and the plane; space curves, derivatives and integrals of vectors, curves, the unit tangent, arc length; surfaces, partial derivatives of vectors, the gradient vector, vector fields, vector differential operators; line integrals, gradient fields; surface integrals in the plane, Green's theorem, surface integrals in space, Stokes' theorem; volume integrals; Gauss' divergence theorem; centres of mass and moments of inertia. Die reguitlyn en platvlak; ruimtekrommes, afgeleides en integrale van vektore, krommes, die eenheidstangente, booglengte, vlakke, parsiële afgeleides van vektore, die gradiëntvektor, vektorvelde, vektordifferensiaaloperatore; lynintegrale, gradiëntvelde; oppervlakintegrale in die platvlak, Green se stelling, oppervlakintegrale in die ruimte, Stokes se stelling; volumeintegrale; Gauss se divergensiestelling; massamiddelpunte en traagheidsmomente.

Appl. Maths for Civil Engineers TW vir Siviele Ingenieurs (TWB252)
(2ndde semester)
Mr Josias

Mathematical modelling: correct identification of problems and specification of assumptions; formulation of ordinary and partial differential equations; analytical solutions; interpretation of a solution in terms of the initial problem. Wiskundige modellering: korrekte identifisering van probleme en spesifisering van aannames; formulering van gewone en parsiële differensiaalvergelykings; analitiese oplossings; interpretasie van ’n oplossing aan die hand van die oorspronklike probleem.

Numerical MethodsNumeriese Metodes (NM262)
(2ndde semester)
Prof Weideman

Introduction to Matlab; zeros of functions; solving of systems of linear equations; numerical differentiation and integration; interpolation and curve fitting; numerical methods for solving ordinary and partial differential equations. Inleiding tot Matlab; nulpunte van funksies; oplos van stelsels van lineêre vergelyings; numeriese differensiasie en integrasie; interpolasie en krommepassing; numeriese metodes vir die oplos van gewone en parsiële differensiaalvergelykings.

Other modulesAnder modules

Some of the honours-level modules offered by Applied Mathematics may be applicable to 4th-year or postgraduate engineering students. Information can be found under postgraduate studies. Sommige van die honneursmodules wat deur Toegepaste Wiskunde aangebied word, mag van toepassing wees vir 4de-jaar of nagraadse ingenieurstudente. Inligting kan by nagraadse studies gevind word.