Page 154 - FINAL_HANDBOOK_20242025

Faculty of Science Handbook, Academic Session 2024/2025

Absolute and relative SIM2001
addressing, Excel functions. ADVANCED CALCULUS
Graph plotting. Use of Excel
Solver. Applications to some Partial derivatives.
selected mathematical Differentiability and continuity.
problems. Linearization and differentials.
The Chain Rule, Partial
Assessment: derivatives with constrained
Continuous Assessment: 50% variables. Directional
Final Examination: 50% derivatives. Gradient,
divergence and curl. Tangent
planes. Taylor’s Theorem.
SIM1006 Extremum problems of
ORDINARY DIFFERENTIAL functions of two variables.
EQUATIONS Lagrange multipliers.

First-order ODEs: Definitions, Double integrals, iterated
solution concepts, valid integrals and Fubini’s
solution intervals. Solutions to Theorem. Applications to areas
separable equations, linear and volumes. Double integrals
equations, Bernoulli, exact and in polar form. Triple integrals,
non-exact, homogeneous iterated integrals. Volumes and
equations. Some applications masses. Triple integrals in
of first-order ODEs. cylindrical and spherical
coordinates forms. Substitution
Linear ODEs of second and in multiple integrals, Jacobians.
higher orders: Definitions,
solution concepts, linear Basic set theory. Functions,
independence, Wronskian. bijective functions, inverse
Solutions to homogeneous and functions. Finite and infinite
non-homogeneous equations. sets, countable and
Method of undetermined uncountable sets. The Real
coefficients, Variation of Number system. Bounds,
parameters. Series solutions. supremum and infimum.
Frobenius’s method, Legendre Archimedean property.
and Bessel’s equations. Rational and irrational
Assessment: numbers. Properties of real
Continuous Assessment: 40% numbers. Sequences of real
Final Examination: 60% numbers, convergence. Limit
Theorems. Monotone
sequences, Cauchy
sequences and subsequences.
Basic topology of the real line:

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