This 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 the following module collections.
Method of assessment
80% examination and 20% coursework.
E. Kreyszig, Advanced Engineering Mathematics (10th edition), John Wiley, 2011
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes.
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.
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Credit level 4. Certificate level module usually taken in the first stage of an undergraduate degree.
- ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
- The named convenor is the convenor for the current academic session.
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