This module introduces widely-used mathematical methods for functions of a single variable. 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.
Complex numbers: Complex arithmetic, the complex conjugate, the Argand diagram, de Moivre's Theorem, modulus-argument form; elementary functions
Polynomials: Fundamental Theorem of Algebra (statement only), roots, factorization, rational functions, partial fractions
Single variable calculus: Differentiation, including product and chain rules; Fundamental Theorem of Calculus (statement only), elementary integrals, change of variables, integration by parts, differentiation of integrals with variable limits
Scalar ordinary differential equations (ODEs): definition; methods for first-order ODEs; principle of superposition for linear ODEs; particular integrals; second-order linear ODEs with constant coefficients; initial-value problems
Curve sketching: graphs of elementary functions, maxima, minima and points of inflection, asymptotes
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 a single variable;
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: polynomials, differentiation, integration, elementary solution methods for scalar ODEs, curve sketching;
3 apply the underlying concepts and principles associated with basic single-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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