MA4051 - Calculus (2024/25)
| Module specification | Module approved to run in 2024/25 | ||||||||||||
| Module title | Calculus | ||||||||||||
| Module level | Certificate (04) | ||||||||||||
| Credit rating for module | 15 | ||||||||||||
| School | School of Computing and Digital Media | ||||||||||||
| Total study hours | 150 | ||||||||||||
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| Assessment components |
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| Running in 2024/25(Please note that module timeslots are subject to change) |
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Module summary
The module covers basic mathematical techniques of differential and integral calculus. The module builds on and extends concepts learned in A-Level Mathematics. The contents covered and the skills developed are fundamental to the development of mathematical competence. Calculus forms an important foundation for further studies in Mathematics, Finance, Statistics and Engineering.
Prior learning requirements
A Level Mathematics.
Available for Study Abroad? NO.
Syllabus
Functions and their graphs. LO1
Differentiation techniques. Applications of differentiation. LO2
Integration techniques. Applications of integration. LO3
Balance of independent study and scheduled teaching activity
This module will be delivered through a mixture of lectures and tutorials. The lectures will develop theory, explain the methods and techniques, and demonstrate them by going through examples. The tutorials will provide students with the opportunity of reviewing their lecture notes and working through the problems designed for their practice, which will underpin the skills and techniques demonstrated in the lectures. Students will be encouraged to construct valid and precise mathematical arguments and will be expected to produce solutions using appropriate notational and stylistic conventions. Self-study exercises will enable students to monitor their own progress. A set of lecture notes will be provided to students and answers for exercise questions will be put on the VLE. Blended learning is incorporated by using online resources as a medium for communication (both peer and tutor-led) and will also provide additional materials to stimulate the student interest and broaden their horizons.
Learning outcomes
On successful completion of this module, students should be able to:
LO1. Demonstrate an understanding of functions and their properties, domain and range, inverse functions, limits, continuity and l'Hopital's rule.
LO2. Differentiate functions from first principles. Demonstrate skill in use of the rules of differentiation (chain, product, quotient).
LO3. Establish skill in use and application of the definite integral. Anti-derivatives and the indefinite integral. Fundamental Theorem of Calculus. Rules and techniques for integration: partial fractions, by parts, by substitution. Improper integrals.
Bibliography
Core Textbooks:
Stewart, J. (2005); Calculus. Brook/Cole
Additional Reading:
Stroud, K.A. (2010); Engineering Mathematics. Macmillan