Page 139 - FULL FINAL HANDBOOK 20232024

Faculty of Science Handbook, Academic Session 2023/2024

SYNOPSIS OF COURSES tests, absolute convergence, the ratio and root tests,
alternating series test, conditional convergence, power
SIX1016 STATISTICS (FACULTY OF SCIENCE) series, Taylor and Maclaurin series. Calculus with
parametric curves, polar coordinates. Three-
Introduction to statistics; Experimental and observational dimensional coordinate systems, vectors, the dot
studies; Display and organisation of data; Descriptive product, the cross product, triple product, lines and
statistics; Population and samples; Sampling methods; planes, cylinder and quadric surfaces. Vector-valued
Basic probability theory; Useful probability distributions: functions, space curves, derivatives and integrals of
binomial, Poisson and normal; Sampling distributions; vector functions.
Central Limit Theorem; Point estimation and confidence
interval; Hypothesis testing for mean and proportion in Assessment:
one and two populations; Chi-square tests; Simple linear Continuous Assessment: 40%
regression and correlation analysis. Final Examination: 60%
Assessment:
Continuous Assessment: 100%
SIM1004 FUNDAMENTALS OF COMPUTING
MATLAB - Matlab environment, matrices, constants and
SIM1001 BASIC MATHEMATICS variables, operations, built-in functions, formatted
output, plotting graphs, expressions and logical data,
Introductory logic. Mathematical statements. Quantifiers. branches and loops, scripting, user-defined functions.
Rules of inference. Mathematical induction, binomial Applications to selected mathematical problems.
theorem. Sets, Cartesian products, equivalence
relations, functions, bijections, inverse functions. Assessment:
Integers, rational numbers, real numbers. Complex Continuous Assessment: 50%
numbers. De Moivre’s theorem and roots of unity. Final Examination: 50%
Polynomials and equations. Remainder theorem,
fundamental theorem of algebra, conjugate roots.
Systems of linear equations, row reduction, echelon SIM1005 FUNDAMENTALS OF SPREADSHEETS
forms. Matrix operations, algebraic properties of
matrices, inverses, elementary matrices, linear Basics of worksheets, entering labels, numbers and
independence and homogeneous linear systems, formulae. Absolute and relative addressing, Excel
matrices with special forms. Determinants, cofactor functions. Graph plotting. Use of Excel Solver.
expansion, properties of determinants, Cramer’s rule, Applications to some selected mathematical problems.
eigenvalues, eigenvectors, and diagonalization.
Assessment:
Assessment: Continuous Assessment: 50%
Continuous Assessment: 40% Final Examination: 50%
Final Examination: 60%
SIM1006 ORDINARY DIFFERENTIAL EQUATIONS
SIM1002 CALCULUS I
First order ODEs: Definitions, solution concepts, valid
Functions and their graphs, combining functions, solution intervals. Solutions to separable equations,
trigonometric functions. Rate of change and tangent linear equations, Bernoulli, exact and non-exact,
lines to curves, limits of functions and limit laws, the homogeneous equations. Some applications of first
precise definition of a limit, one-sided limits, continuity, order ODEs.
limits involving infinity and asymptotes of graphs.
Tangent lines and the derivative at a point, the derivative Linear ODEs of second and higher orders: Definitions,
as a function, differentiation rules, derivatives of solution concepts, linear independence, Wronskian.
trigonometric functions, the chain rule, implicit Solutions to homogeneous and non-homogeneous
differentiation. Extreme values of functions, the mean equations. Method of undetermined coefficients,
value theorem, monotonic functions and the first Variation of parameters. Series solutions. Frobenius’s
derivative test, concavity and curve sketching, method, Legendre and Bessel’s equations.
antiderivatives. Sigma notation and limits of finite sums,
the definite integral, the fundamental theorem of Assessment:
calculus, indefinite integrals and the substitution method, Continuous Assessment: 40%
the definite integrals substitution and the area between Final Examination: 60%
curves, logarithms functions, exponential functions,
indeterminate forms and L’hopital’s Rule.
Assessment: SIM2001 ADVANCED CALCULUS
Continuous Assessment: 40%
Final Examination: 60% Partial derivatives. Differentiability and continuity.
Linearization and differentials. The Chain Rule, Partial
derivatives with constrained variables. Directional
derivatives. Gradient, divergence and curl. Tangent
SIM1003 CALCULUS II planes. Taylor’s Theorem. Extremum problems of
functions of two variables. Lagrange multipliers.
Inverses trigonometric functions, hyperbolic functions,
inverses hyperbolic functions. Basic integration Double integrals, iterated integrals and Fubini’s
formulas, integration by parts, trigonometric integrals, Theorem. Applications to areas and volumes. Double
trigonometric substitutions, integration of rational integrals in polar form. Triple integrals, iterated integrals.
functions by partial fractions, improper Integrals. Volumes and masses. Triple integrals in cylindrical and
Sequence, infinite series, the integral test, comparison spherical coordinates forms. Substitution in multiple
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