MATH1042A - Engineering Mathematics IA
Course coordinators:
Course credits: 18
Prerequisites
The minimum entry requirement is 60% in Matric (and AS-level, HIGCSE, International Bacculareate, …) and a D in A-levels. Depends on registration in one of the faculty of engineering programmes.
MATH1042A is a 12-week first-semester course and forms the basis of knowledge and skills required in MATH1043A. MATH1042A is a prerequisite for MATH1043A – Engineering Mathematics IB.
Course aims:
The main purpose of this course is to provide students with a basic foundation in differentiation and integration techniques with simple applications, the binomial theorem, simple series and the conic sections in preparation for further study in Engineering Mathematics IB.
Topics in Calculus include: Functions; Domain and range of functions; composite functions; Limits and continuity; Differentiation; Applications of differentiation (curve sketching, maxima and minima and rates of change); Antiderivatives, definite and indefinite integrals; Riemann sums; Applications of integration to areas and volumes; the natural logarithmic and exponential functions (transcendental functions).
Topics in Algebra include: Radian measure; trigonometric functions; trigonometric equations; polar coordinates; the principle of mathematical induction; Binomial Theorem; conic sections.
MATH1043A - Engineering Mathematics IB
Course coordinators:
Course credits: 18
Prerequisites:
MATH1042A is a prerequisite for MATH1043A – Engineering Mathematics IB. MATH1043 is a 12 week second semester course and builds on the knowledge and skills acquired in MATH1042A.
Course aims:
The main purpose of this course is to provide the students with a basic foundation in differentiation and integration techniques and simple application, the solution of simple differential equations and matrices.
Topics in Calculus 1B include: Further techniques of integration and Improper integrals; Sequences and series; Taylor and Maclaurin series; L’Hôpital’s rule; Partial differentiation; Ordinary first order differential equations.
Topics in Algebra 1B include: Linear systems of equations; Gaussian elimination; matrix algebra; inverse matrices; determinants; inverse matrices by elementary row operations and adjoint-determinant method; Cramer’s rule; dot product and cross product in R3; Vector algebra in R2 and R3; lines and planes in R3 ; complex numbers; modulus argument form of complex numbers; De Moivre’s Theorem; n-th roots.
Course coordinators
Prerequisites and possible destinations
- Prerequisites: MATH1042 and MATH1043
- Possible destinations: MATH 2 Major, MATH3025/3026
Courses
MATH2011 is a second-year engineering maths course having 4 lectures and 1 tutorial per week. The course has two components: algebra and calculus.
Schools: Chemical, Mechanical, Aeronautical, Industrial, Science.
ALGEBRA (MATH2011)
A continuation of complex numbers from first year work and convergence of series. The linear algebra section includes: eigenvalues and eigenvectors; the Cayley-Hamilton theorem and applications to differential equations; change of coordinates, diagonalisation and applications; orthonormality, unitary and hermitian matrices and quadratic forms; Fourier series; Domains in the complex plane, analytic functions and Cauchy-Riemann equations.
CALCULUS (MATH2011)
Starts with the solution of linear differential equations using D-operator methods. The section on vector differentiation includes curvature, trajectories, directional derivatives, grad, div and curl, streamlines and potential functions, classification of surfaces. Vector integration includes path integrals, double integrals, Jacobians, Green's theorem in the plane.
MATH2026 is a second year engineering maths course having 4 lectures and 1 tutorial per week in the first semester only. The course has two components: algebra and calculus.
Schools: Civil, Metallurgy, Mining
ALGEBRA (MATH2026)
A continuation of complex numbers from first year work and convergence of series. The linear algebra section includes: eigenvalues and eigenvectors; the Cayley-Hamilton theorem and applications to differential equations; change of coordinates, and diagonalisation and its applications.
CALCULUS (MATH2026)
This consists of the solution of linear differential equations using D-operator methods followed by a section on vector differentiation which includes curvature, trajectories and orthogonal trajectories.
MATH2014 is a second year engineering maths course having 6 lectures and 2 tutorials per week in the first semester, and 4 lectures and 1 tutorial per week in the second semester. The course has three components: algebra, calculus and transforms.
Schools: Electrical, Biomed, Digital
ALGEBRA (MATH2014)
A continuation of complex numbers from first year work and convergence of series. The linear algebra section includes: eigenvalues and eigenvectors; the Cayley-Hamilton theorem and applications to differential equations; change of coordinates, diagonalisation and applications; orthonormality, unitary and hermitian matrices and quadratic forms; Fourier series; Domains in the complex plane, analytic functions and Cauchy-Riemann equations.
CALCULUS (MATH2014)
Starts with the solution of linear differential equations using D-operator methods. The section on vector differentiation includes curvature, trajectories, directional derivatives, grad, div and curl, streamlines and potential functions, classification of surfaces. Vector integration includes path integrals, double integrals, Jacobians, Green's theorem in the plane.
TRANSFORMS (MATH2014)
Introduces Laplace transforms and explains their use in extending second year results on D-operators and stability. Special functions that arise naturally are also discussed, as are Fourier transforms, which are related to both Laplace transforms and Fourier series. Finally, various analytic techniques for solving certain partial differential equations are covered.
Mathematics III (Engineering) MATH3036 and MATH3025/3026
MATH3036
Mathematics Methods
Course coordinator: Professor Abdul Kara
Prerequisites: MATH2011/2026/2014
The topics Laplace Transforms, Linear Programming, Game Theory and Markov Chains are offered at third-year level to Industrial Engineering students.
MATH3025/3026
Third year (Engineering) topics Math3025/3026
Course coordinator: Professor Abdul Kara
Prerequisites: MATH2011 or MATH2014
The topics Transforms and Special Functions, Complex Variables and Integral Theorems, and Applied Complex Variables are offered at third or fourth-year level to various branches of Engineering.
Transforms and Special Functions
Introduces Laplace transforms and explains their use in extending second year results on D-operators and stability. Special functions that arise naturally are also discussed, as are Fourier transforms, which are related to both Laplace transforms and Fourier series. Finally, various analytic techniques for solving certain partial differential equations are dealt with.
Complex Variables and Integral Theorems
Starts with functions of a complex variable, which describe transformations of the complex plane. Differentiability properties are discussed, as well as applications to vector fields and stability. The later section consists of surface integrals (i.e., double integrals over not necessarily plane regions), triple integrals (i.e., integrals over solid regions), and the theorems connecting them (which are generalisations of Green s theorem).
Applied Complex Variables
Covers integration of functions of a complex variable with many applications, including the evaluation of real series and integrals, and the analytic inversion of Laplace transforms. Extra examples of inverse Laplace transforms are here.
