UNIVERSITY OF NAMIBIA CENTRE FOR EXTERNAL STUDIES ...

Calculus IISMAT3612NQF Level: 6 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: SMAT3512 – Precalculus and SMAT3511 – Basic Mathematics and SMAT3531 Analytic Geometry, Complex Numbersand MatricesModule description:Integration: Riemann sums, approximations of the definite Riemann integral using the trapezoidal rule and Simpson’s rule. Integrationtechniques: integration by parts, integration of rational functions. Applications of the definite Riemann integral: volume of a solid ofrevolution, arclength, surface of revolution. Partial differentiation, chain rule, directional derivative. Sequences and series of numbers: thelimit of a sequence, absolutely convergent series, tests of convergence. Power series: radius of convergence, interval of convergence,Taylor series, binomial theorem.Euclidean GeometrySMAE3892NQF Level: 8 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: SMAT3611 - Calculus I and SMAE3791 - Functions of a Single Variable IModule description:Incidence structures, principle of double counting and applications thereof. Affine planes: parallel classes, order of an affine plane,isomorphisms and collineations. The real affine plane R 2 : theorem of Desargues, theorem of Pappus, ratios, examples of affinities. Thereal Euclidean plane R 2 : orthogonality of lines, distances, motions, reflections in points and lines.Functions of Single Variable ISMAE3771NQF Level: 7 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: SMAT3611 - Calculus I and SMAT3612 - Calculus IIModule description:Upper and lower bounds of a set of real numbers, supremum and infimum, completeness property of R, Archimedean property of R.Sequences of real numbers: bounded sequences, convergent sequences, Cauchy sequences, limit rules, subsequences. Series of realnumbers: Cauchy criterion, convergent tests. Limit of a function, continuous functions, intermediate value theorem. Differentiation:definition and rules of differentiation.Functions of Single Variable IISMAE3772NQF Level: 7 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: SMAT3611 - Calculus I and SMAT3612 - Calculus IIModule description:Mean value theorem and applications thereof, derivatives of higher order, infinitely differentiable functions, polynomials, Taylor’s theorem,local extrema, convex and concave functions. Riemann integration: upper and lower Darbaux sums, Riemann integrable functions,examples of functions which are not Riemann integrable, Fundamental Theorem of Calculus, integration by substitution, integration byparts.PrecalculusSMAT3512NQF Level: 5 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: IGCSE MathematicsModule description:Functions: one-to-one and onto functions, horizontal line test, composition of functions, inverse of a function. Introduction to exponentialand logarithmic functions. Limit of a function: definition, left and right limits, infinite limits, limits at infinity, continuity in terms of limits.Differentiation: rate of change, derivative of a function, rules of differentiation, increasing and decreasing functions and graph sketching.Integration: antiderivatives, the definite integral, area under a graph. Trigonometry: further trigonometric identities, area of a sector andsegment of a circle, derivatives and integrals of trigonometric functions.Physical SyllabiChemistry IASCHM3511NQF Level: 5 Credits: 16 Module Assessment: CA 50% Examination 50% - 1 x 3 hour paperPrerequisite: Faculty Entry RequirementsModule description:This module is a brief introduction to general chemistry and it lays the foundation of basic facts necessary for further studies in chemistry.The following topics are covered:175