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| Module Availability |
| Semester 1 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: 1 class test
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25
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Exam, 2 hours
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75
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.
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| Module Overview |
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| Prerequisites/Co-requisites |
| None. |
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| Module Aims |
| This module provides techniques, methods and practise in manipulating mathematical expressions using algebra and calculus, building on and extending the material of A-level syllabus. |
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| Learning Outcomes |
At the end of the course a student should have revised and strongly reinforced the skills found in the A-level syllabus and should be able to:
• Understand set notation and know the basic properties of real numbers;
• Analyse and manipulate functions and sketch the graph of a function in a systematic way;
• Differentiate functions by applying standard rules;
• Obtain Taylor & Maclaurin series expansions for a variety of functions;
• Evaluate integrals by means of substitution, integration by parts, partial fractions and other techniques
• Apply differentiation and integration techniques to a variety of theoretical and practical problems;
• Solve first order ordinary differential equations and second order ordinary differential equations with constant coefficients.
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| Module Content |
• Exponential, logarithmic, trigonometric and hyperbolic functions.
• Properties and types of functions. Inverse, parametric and implicit functions .Limits.
• Equations. Plane polar coordinates. Curve sketching. Transformation of curves.
• Techniques of differentiation - parametric, implicit, logarithmic and partial derivatives.
• Applications of differentiation. l’Hôpital’s rule.
• Power series, manipulation and application. Taylor and Maclaurin series.
• Techniques of integration; reduction formulae; arc length, areas of surfaces and volumes of revolution.
• First order ODEs. Separation of variables. Integrating factor method. Homogeneous equations. Bernoulli equations. Initial value problems. Series solutions.
• Second order linear ODEs with constant coefficients. |
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| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and tests. Learning takes place through lectures, tutorials, tests and exercise sheets:
44 hours of lectures and tutorials over 11 weeks in semester 1.
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| Selected Texts/Journals |
Recommended Reading:
J. Gilbert and C. Jordan : Guide 2 Mathematical Methods, Palgrave Macmillan (2002), ISBN 0333794443.
Further Reading:
Robert A. Adams : Calculus – A Complete Course (5th Ed.), Addison-Wesley (2002), ISBN 0201791315.
Howard Anton et al: Calculus Late Transcendentals (9th Ed). John Wiley (2010), ISBN 9780470398746
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| Last Updated |
| 21 April 2011 |
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