Mathematical Methods - entry

This module will introduce you to key mathematical tools and techniques essential to your further studies. This will include differential and integral calculus, computing limits and convergence of sequences and series, geometry and the fundamentals of vectors and matrix algebra.

This module aims to develop your skills and techniques in calculus, geometry and algebra. It is primarily focused on developing methods and skills for accurate manipulation of the mathematical objects that form the basis of much of an undergraduate course in mathematics. Whilst the main emphasis of the module will be on practical methods and problem solving, all results will be stated formally and each sub-topic will be reviewed from a mathematically rigorous standpoint. The techniques developed in this course will be essential to much of your undergraduate degree programme, particularly the second-year streams of Analysis, Differential Equations & Vector Calculus, and Mathematical Modelling.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 explain how techniques in differential and integral calculus are underpinned by formal rigour;
2 apply techniques in geometry and algebra to explore three dimensional analytic geometry;
3 perform accurate manipulations in algebra and calculus of several variables using a variety of standard techniques;
4 solve some specific classes of ordinary differential equations;

Discipline Specific Skills and Knowledge:
5 demonstrate a basic knowledge of functions, sequences, series, limits and differential and integral calculus necessary for progression to successful further studies in the mathematical sciences;
Personal and Key Transferable/ Employment Skills and  Knowledge:
6 reason using abstract ideas, and formulate and solve problems and communicate reasoning and solutions effectively in writing;
7 use learning resources appropriately;
8 exhibit self management and time management skills.

Geometry: lines; planes; conic sections.

Functions: single- and multivariate; limits; continuity; intermediate value theorem.

Sequences: algebra of limits; L'Hopital's rule.

Series: convergence/divergence tests; power series.

Differential calculus: simple and partial derivatives; Leibniz' rule; chain rule; Taylor approximation; implicit differentiation; minima and maxima.

Integral calculus: substitution; integration by parts; multiple integrals; applications.

Differential equations: linear and separable ordinary DEs; basic partial DEs.

Vectors, matrices: Gaussian elimination; transformations; eigenvalues/eigenvectors.

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.


If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

Basic reading: Any A-level on mathematics and further mathematics

ELE: http://vle.exeter.ac.uk

Reading list for this module: