Page 245 - FINAL_HANDBOOK_20252026

Faculty of Science Handbook, Academic Session 2025/2026

SIF1017 MATHEMATICAL METHODS I (3 problems including constraints; Lagrange
CREDITS) multipliers, endpoint and boundary point
problems; change of variables;
Differentiation: Differentiation from first differentiation of integrals, Leibniz rule.
principle: products; the chain rule;
quotients; implicit differentiation; Assessment Method:
logarithmic differentiation; Leibnitz’ Summative 60%
theorem; special points of a function; Assessment:
curvature; theorems of differentiation Continuous 40%
Assessment:
Integration: Integration from first
principles: the inverse of differentiation; SIF1018 MATHEMATICAL METHODS II (4
by inspection; sinusoidal functions; CREDITS)
logarithmic integration; using partial
fractions; substitution method; Mutliple integrals: integrated integrals;
integration by parts; reduction formulae; applications of Integrations; double and
infinite and improper integrals; plane triple integrals in cartesian coordinates;
polar coordinates; integral inequalities; double and triple integrals in polar
applications of integration coordinates; change of variables in
integrals; Jacobian; surface integrals.
Complex number: Real and imaginary
parts of complex number; complex plane; Vector analysis: applications of vector
complex algebra; complex infinite series; multiplication; triple products;
complex power series; elementary differentiation and partial differentiation
functions of complex numbers; Euler’s of vectors; integration of vectors; scalar
formula; powers and roots of complex and vector fields; directional derivative;
numbers; exponential and trigonometric unit normal vectors; gradient; divergence
functions; hyperbolic functions; of a vector function; curl of a vector
logarithms; complex roots and powers; function; Laplacian; vector operators in
inverse trigonometric and hyperbolic polar coordinates; line integrals: scalars
functions; and vectors; Green’s Theorem in a plane;
divergence and divergence theorem; Curl
Matrices and solutions for sets of linear and Stoke’s Theorem.
equations: matrix and row reduction;
Cramer’s rule; vectors and their notation; Tensors: coordinate-system
matrix operations; linear combinations, transformation; basis vector
linear functions, linear operators; matrix transformation; non-orthogonal
operators, Linear transformation, coordinate systems; dual basis vectors;
orthogonal transformation, eigen value finding covariant and contravariant
and eigen vector and diagonalization of components; index notation; quantities
matrices; special matrices. that transform contravariantly and
covariantly; concepts of covariance and
Partial differentiation: power series in two contravariance beyond vectors; covariant,
variables; total differentials; chain rule; contravariant, and mixed tensors; tensor
implicit differentiation; stationary values addition and subtraction; tensor
of a function with one variable and two multiplication; metric tensor; general
variables; application of partial curvilinear coordinates; index raising and
differentiation to maximum and minimum lowering; tensor derivatives and

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