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

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, Dr Diedericks, Mr Crous, 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

Kinematics in one and two dimensions; relative velocities; the equations of motion; rectilinear motion with constant forces; forces in a plane; parabolic motion; circular motion; the principle of work and energy; power; conservation laws; impulse and momentum; angle impulse and angle momentum; kinetics of particle systems. Kinematika in een en twee dimensies; relatiewe snelhede; die bewegingsvergelykings; reglynige beweging met konstante kragte; kragte in die plat vlak; paraboliese beweging; beweging in 'n sirkelbaan; arbeid-energiebeginsel; drywing; behoudswette; impuls en momentum; hoek-impulse en hoemmomentum; kinetika van partikelstelsels.

### Second yearTweede jaar

 20753-224 Dynamics of Rigid BodiesDinamika van Starre Liggame (TWB224) (1ste semester) Prof. Smit, Dr Coetzer, Dr Cloete

Plane kinetics of rigid bodies; rotation and translation; absolute and relative motion; instantaneous centre of zero velocity. Properties of rigid bodies; definite and multiple integrals; Cartesian, polar, cylindrical and spherical coordinate systems; areas, volumes, centres of mass and moments of inertia. Newton's laws; energy methods. Introduction to three-dimensional dynamics of rigid bodies. Vibrations of rigid bodies. Vlakkinetika van starre liggame; rotasie en translasie; absolute en relatiewe beweging; oombliklike rotasie-as. Eienskappe van starre liggame; bepaalde en meervoudige integrale; Cartesiese, pool-, silindriese en sferiese koördinaatstelsels; areas, volumes, massamiddelpunte en traagheidsmomente. Newton se wette; energiemetodes. Inleiding tot drie-dimensionele dinamika van starre liggame. Vibrasies van starre liggame.

 20753-242 Vector Analysis Vektoranalise (TWB242) (2ndde semester) Dr Diedricks, 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) Dr Coetzer

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, Dr Hale

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.

### Third yearVierde jaar

 20753-834 Partial Differential EquationsParsiële Differensiaalvergelykings (TWB834) (1ste semester) Dr Cloete

Derivation of simple partial differential equations (PDEs) from first principles, Fourier analysis, separation of variables and transform techniques for linear second-order PDEs, characteristics, Lagrange's method for first-order PDEs, finite differences. Herleiding van eenvoudige parsiële differensiaalvergelykings (PDVs) uit eerste beginsels, Fourier analise, skeiding van veranderlikes en transform-tegnieke vir lineêre tweede-orde PDVs, karakteristieke, Lagrange se metode vir eerste-orde PDVs, eindige verskille.

### 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.