This module introduces widely-used mathematical methods for matrix operations, calculus of functions of a single variable, and scalar ordinary differential equations (ODEs). 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.
Basic notation for sets and number systems including complex numbers (a+ib representation only). Standard functions: trig functions, polynomials, rational functions, exponentials and logarithms.
Algebra of matrices and vectors; addition, multiplication, transposes, inner-products. Row reduced echelon form, solving linear systems (homogeneous and inhomogeneous). Inverse of a matrix.
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.
Curve sketching: graphs of elementary functions, maxima, minima and points of inflection, asymptotes. Taylor approximations, integrals with a parameter, multiple integrals, changing integration order.
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.
Use of ODEs in mathematical modelling in mathematical biology and/or Newtonian mechanics.
Contact hours: 88
Private study: 212
Total: 300
Coursework 40%
Examination 60%
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The most up to date reading list for each module can be found on the university's reading list pages.
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 of algebraic operations with matrices and vectors, calculus of functions of a single variable, elementary solutions of scalar ODEs, and applications of ODEs in mathematical modelling.
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts of matrices and vectors, single variable calculus, elementary solutions of scalar ODEs, and applications of ODEs in mathematical modelling, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material;
3 apply the underlying concepts and principles associated with matrix operations, basic single-variable calculus techniques, and scalar ODE's in several well-defined contexts, showing an ability to evaluate the appropriateness of different approaches to solving problems in this area;
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);
7 communicate technical and non-technical material competently.
8 demonstrate an increased level of skill in numeracy and computation.
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