Download Mathematics Module description

English Language Centre
International Science Foundation Programme
2014-15
Mathematics
Module description
This module will provide you with an in-depth introduction to major mathematics topics
required for successful undergraduate study. The module is delivered through a
combination of theoretical lectures and problem-solving tutorials. These will support you in
manipulating your knowledge of these key concepts so that you are able to apply them and
discuss them in familiar contexts. This will also support you in beginning to understand
more complex applications.
Educational aims
By the end of the module, you will:
 Have the mathematical background knowledge to start an undergraduate
programme in mathematics, physics, computer science, engineering or a related
subject.
 Have the understanding of mathematical techniques to solve simple problems in
these subjects.
 Understand which mathematical techniques are appropriate for any given simple
problem.
 Be equipped to suggest ways to model mathematically simple concepts in physical
and economic sciences.
Assessment
You are assessed through a combination of coursework (30%) and final exam (70%).
English Language Centre
International Science Foundation Programme
2014-15
Module structure
During this module, you will cover key issues in the following areas:










Algebra: indices; identities and inequalities; partial fractions; quadratic equations;
logarithms; logarithmic equations; remainder and factor theorems; binomial
theorem; Pascal’s triangle;
Functions: mappings, domains and ranges; exponential and logarithmic functions;
inverse functions; modulus function; even, odd and periodic functions; curve
sketching;
Coordinate geometry: equation of a straight line; distances and midpoints; quadratic
curves; intersections of curves;
Trigonometry: radians; trigonometric functions, relationships and identities;
graphical representation; “special” angles; trigonometric equations;
transformations of trigonometric functions; sine and cosine rules; hyperbolic
functions, relationships and identities;
Differential calculus: differentiation from first principles; differentiation of: powers
of x, polynomials, exponential, logarithmic and trigonometric functions; product,
quotient and chain rules; small increments and rates of change; gradients, tangents
and normals; stationary points (maxima, minima and points of inflection);
Integral calculus: fundamental theorem of calculus; integration of: powers of x,
polynomials, 1/x, exponential and trigonometric functions; integration by parts;
further integration techniques; indefinite and definite integrals; boundary conditions;
limit of a sum; area under/between curves; volumes of revolution;
Differential equations: first order; separation of variables; boundary conditions;
Vectors: two and three dimensions; components; addition, subtraction and scalar
multiplication; direction ratios and cosines; unit and direction vectors; geometrical
properties; equations of lines and planes; distances/angles between points/planes;
scalar and vector products;
Sequences and series: sequences, series and notation; arithmetic and geometric
progressions; convergence of series; sums to n and infinity (for convergent
geometric series); tests for convergence;
Complex numbers: imaginary numbers; algebraic properties; complex roots of
quadratic equations;
Please note that the module content requires you to have a good basic background in
algebra, trigonometry and geometry.
Students following this module also follow either the Physics, Chemistry, or Business
Management modules.