Mathematical Methods and Applications

Module code: ENM4004-B

SEMESTER 1

Algebra: manipulation, linear and quadratic equations; powers and roots; exponential and logarithmic forms.
Co-ordinate geometry: 2D Cartesian and polar coordinates, familiar geometric shapes and equations (line, circle, ellipse, hyperbola). Parametric curves. 3D Cartesian and spherical coordinates.
Functions: concepts and notation, graphs of specific functions (polynomial, trigonometric, exponential, logarithm), transformations, composition, inverses, hyperbolic functions. Limits: Differentiation: definitions, tables, rules (sum, product, quotient, chain), techniques
(implicit, parametric, logarithmic), application to engineering (e.g. related rates, maxima and minima).

WEEK 7 FORMATIVE TEST (2ND HOUR)

Integration: definitions, tables, rules, techniques (substitution, by parts), application to engineering (e.g. area, surface and volume of rotation, arc length, centroid, mean value). Complex numbers: properties, algebra, polar and exponential forms, roots, loci, application to engineering.

WEEK 11 (SKILLS FOR ENGINEERS LABS)

Vector algebra: properties, unit vector, lines and planes, i,j,k, scalar product, vector product, applications to engineering (e.g. forces, work done, moments).
Matrix algebra: definitions, basic algebra, linear transformations, linear systems.

SEMESTER 2

WEEK 1 FORMATIVE (1ST & 2ND HOUR)

Matrix algebra: eigenvalues and eigenvectors, applications to engineering (e.g. material deformation).

WEEK 4 REVISION

Ordinary Differential Equations: 1st-order ODEs (direct, separable, linear and integrating factor), specific non-linear ODEs, constant-coefficient 2nd-order ODEs (complementary function, particular integral), application to engineering.
Sequences: sequences, series and power series.
Numerical methods: errors, solution to equations, numerical integration.

WEEKS 8 AND 9 REVISION

WEEK 10 FORMATIVE (1ST & 2ND HOUR)

WEEKS 11 AND 12 REVISION