ENGINEERING MATHEMATICS 1

Course Code

EG 1504

Credit Points

15

Course Coordinator

Dr A Sevastyanov

Pre-requisites

Higher Mathematics (Grade B).

Overview

• Revision: Basic differentiation & Integration: Rules of differentiation - sum, product rule. Higher derivatives. Maxima & Minima: The idea and the basic tests, including 2nd derivative tests. Higher derivatives.


• Differential calculus: Chain and quotient rule. The inverse trig functions arcsin, arccos, arctan and their derivatives. Log and exp. Properties and derivatives. Sinh, cosh & tanh. Taylor series approximations.


• Integral Calculus: Basic techniques: substitution, parts, partial fractions. Reduction formulae. Definite integrals. Definite integrals and applications of integration to finding areas, volumes of revolution, lengths of paths, first moments of area and centres of gravity of uniform laminae.


• Complex Numbers: The arithmetic of complex numbers. Argand plane. Modulus, conjugate, argument etc. Polar form and de Moivre's theorem. Solution of zn = 1. Theory of equations: Roots and factors of polynomials. Multiple roots. Fundamental theorem of Algebra. Complex roots of real polynomials occur in conjugate pairs. The Fourier matrix and applications.

Structure

30 one-hour lectures, 1 one-hour tutorial per week and 5 two-hour problem solving sessions.

Assessment

1st Attempt: 1 three-hour written examination (80%) and continuous assessment (20%).


Resit: 1 three-hour written examination (80%) and continuous assessment (20%).