Pre-requisite: MAST4006 (Mathematical Methods 1)
OverviewThis module introduces widely-used mathematical methods for vectors and functions of two or more variables. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage. Tutorials and Maple worksheets will be used to support taught material.
Vectors: Cartesian coordinates; vector algebra; scalar, vector and triple products (and geometric interpretation); straight lines and planes expressed as vector equations; parametrized curves; differentiation of vector-valued functions of a scalar variable; tangent vectors; vector fields (with everyday examples)
Partial differentiation: Functions of two variables; partial differentiation (including the chain rule and change of variables); maxima, minima and saddle points; Lagrange multipliers
Integration in two dimensions: Double integrals in Cartesian coordinates; plane polar coordinates; change of variables for double integrals; line integrals; Green's theorem (statement – justification on rectangular domains only)
This module appears in:
Method of assessment
80% examination and 20% coursework.
E. Kreyszig, Advanced Engineering Mathematics (10th edition), John Wiley, 2011
On successfully completing the module students will be able to:
1 demonstrate knowledge of the underlying concepts and principles associated with basic mathematical methods for functions of multiple variables;
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material: vectors, partial differentiation, stationary points of functions, double integration;
3 apply the underlying concepts and principles associated with basic multiple-variable techniques in several well-defined contexts, showing an ability to evaluate the appropriateness of different approaches to solving problems in this area;
4 make appropriate use of Maple.
The intended generic learning outcomes.
On successfully completing the module students will be able to demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle) and Maple;
7 communicate technical and non-technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.