## Applied Mathematics modules for BEng studentsToegepaste Wiskunde modules vir BIng studente 2022

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

 20753-124 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.

 20753-154 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

 20753-224 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.

 20753-242 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.

 20753-252 Appl. Maths for Civil EngineersTW 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.

 36323-262 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.