Page 158 - FINAL_HANDBOOK_20252026

Faculty of Science Handbook, Academic Session 2025/2026

convergence, power series, Taylor and Bernoulli, exact and non-exact,
Maclaurin series. Calculus with parametric homogeneous equations. Some
curves, polar coordinates. Three- applications of first-order ODEs.
dimensional coordinate systems, vectors,
the dot product, the cross product, triple Linear ODEs of second and higher orders:
product, lines and planes, cylinder and Definitions, solution concepts, linear
quadric surfaces. Vector-valued functions, independence, Wronskian. Solutions to
space curves, derivatives and integrals of homogeneous and non-homogeneous
vector functions. equations. Method of undetermined
coefficients, Variation of parameters. Series
Assessment: solutions. Frobenius’s method, Legendre
Continuous Assessment: 40% and Bessel’s equations.
Summative Assessment: 60% Assessment:
Continuous Assessment: 40%
SIM1004 Summative Assessment: 60%
FUNDAMENTALS OF COMPUTING
SIM2001
MATLAB - Matlab environment, matrices, ADVANCED CALCULUS
constants and variables, operations, built-in
functions, formatted output, plotting Partial derivatives. Differentiability and
graphs, expressions and logical data, continuity. Linearization and differentials.
branches and loops, scripting, user-defined The chain rule, partial derivatives with
functions. Applications to selected constrained variables. Directional
mathematical problems. derivatives. Gradient, divergence and curl.
Tangent planes. Taylor’s Theorem.
Assessment: Extremum problems of functions of two
Continuous Assessment: 50% variables. Lagrange multipliers.
Summative Assessment: 50%
Double integrals, iterated integrals and
SIM1005 Fubini’s Theorem. Applications to areas and
FUNDAMENTALS OF SPREADSHEETS volumes. Double integrals in polar form.
Triple integrals, iterated integrals. Volumes
Basics of worksheets, entering labels, and masses. Triple integrals in cylindrical
numbers and formulae. Absolute and and spherical coordinates forms.
relative addressing, Excel functions. Graph Substitution in multiple integrals,
plotting. Use of solvers. Applications to Jacobians.
some selected mathematical problems.
Assessment: Basic set theory. Functions, bijective
Continuous Assessment: 50% functions, inverse functions. Finite and
Summative Assessment: 50% infinite sets, countable and uncountable
sets. The real number system. Bounds,
SIM1006 supremum and infimum. Archimedean
ORDINARY DIFFERENTIAL EQUATIONS property. Rational and irrational numbers.
Properties of real numbers. Sequences of
First-order ODEs: Definitions, solution real numbers, convergence. Limit
concepts, valid solution intervals. Solutions theorems. Monotone sequences, Cauchy
to separable equations, linear equations, sequences and subsequences. Basic

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