Page 263 - FINAL_HANDBOOK_20242025

Faculty of Science Handbook, Academic Session 2024/2025

Differentiation: Differentiation from first principle: products; the chain
rule; quotients; implicit differentiation; logarithmic differentiation;
Leibnitz’ theorem; special points of a function; curvature; theorems of
differentiation

Integration: Integration from first principles: the inverse of
differentiation; by inspection; sinusoidal functions; logarithmic
integration; using partial fractions; substitution method; integration by
parts; reduction formulae; infinite and improper integrals; plane polar
coordinates; integral inequalities; applications of integration
Complex number: Real and imaginary parts of complex number;
complex plane; complex algebra; complex infinite series; complex
power series; elementary functions of complex numbers; Euler’s
formula; powers and roots of complex numbers; exponential and
trigonometric functions; hyperbolic functions; logarithms; complex
roots and powers; inverse trigonometric and hyperbolic functions;

Matrices and solutions for sets of linear equations: matrix and row
reduction; Cramer’s rule; vectors and their notation; matrix
operations; linear combinations, linear functions, linear operators;
matrix operators, Linear transformation, orthogonal transformation,
eigen value and eigen vector and diagonalization of matrices; special
matrices.
Partial differentiation: power series in two variables; total differentials;
chain rule; implicit differentiation; stationary values of a function with
one variable and two variables; application of partial differentiation to
maximum and minimum problems including constraints; Lagrange
multipliers, endpoint and boundary point problems; change of
variables; differentiation of integrals, Leibniz rule.

Assessment Method:
Final Examination: 60%
Continuous Assessment: 40%

SIF1018 MATHEMATICAL METHODS II (4 CREDITS)
Mutliple integrals: integrated integrals; applications of Integrations;
double and triple integrals in cartesian coordinates; double and triple
integrals in polar coordinates; change of variables in integrals;
Jacobian; surface integrals.

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