ENGINEERING MATHEMATICS 1

Course Code

EG 1503

Credit Points

15

Course Coordinator

Dr Henry Tan

Pre-requisites

Higher Mathematics (Grade B)

Co-requisites

None

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.


• 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.


• Matrices: Basic definition and notation (m x n). Algebra of matrices: multiplication by scalar, addition & subtraction, multiplication. Zero matrix, identity matrix, transpose, symmetric & anti- symmetric matrices. The meaning of matrix inversion. Inverse of 2x2 matrix. Determinants, with some work on row & column operations together with general expansion formula. Systems of linear equations. Geometrical interpretation. Discussion of various possibilities: unique solution, no solution, infinitely many solutions. Gaussian reduction: Solution of systems of linear equations by formal Gaussian reduction with partial pivoting down to upper triangular form followed by backsubstitution.

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%).

Formative Assessment

Students will have their continuous assessment work returned to them with markers' comments. There will also be informal formative assessment and feedback in the weekly tutorial sessions.

Feedback

Feedback will be provided by the return of marked coursework, and informal feedback at weekly tutorial sessions.