MA5011 - Further Calculus (2024/25)
Module specification | Module approved to run in 2024/25 | ||||||||||||||||
Module title | Further Calculus | ||||||||||||||||
Module level | Intermediate (05) | ||||||||||||||||
Credit rating for module | 30 | ||||||||||||||||
School | School of Computing and Digital Media | ||||||||||||||||
Total study hours | 300 | ||||||||||||||||
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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 extends the students’ knowledge of the techniques of calculus and introduces the concept of multivariable Calculus as well as calculus of vectors.
This module introduces Vector-Valued Functions and extends ideas of calculus of one dimension to Vector-Valued Functions.
Prior knowledge: MA4010 Calculus and Linear Algebra.
Prior learning requirements
None.
Available for Study Abroad? NO
Syllabus
− Vectors, Vector_Valued Functions. (LO1)
− Partial differentiation. Chain rule. Taylor series. (LO2-3)
− Maxima and minima of functions of more than one independent variable. (LO4)
− Integration over plane areas. Volumes. Change of variables. Jacobians. (LO2 & 5)
Balance of independent study and scheduled teaching activity
Students’ learning is directed via face-to-face learning activities centred on lectures and seminars. There is full provision of documents related to the module in electronic format that can be accessed by students at all times. The documents include lecture notes, slides, guidance to further reading and relevant mathematical packages, and exercises and tests.
Learning outcomes
On successful completion of this module, the student be able to:
LO1. Understand the concept of vector in 2 and 3 dimensions.
LO2. Differentiate and integrate functions of multiple variables.
LO3. Understand chain Rule for functions of 2 variables.
LO4. Identify local maxima/minima for multivariable functions.
LO5. Carry out multiple integrals.
Bibliography
Core Textbooks:
1. Brian E. Blank & Steven G. Krantz (2011) Calculus Multivariable, 2nd Edition, Wiley.
2. Jerrold E. Marsden & Anthony J. Tromba, (2011) Vector Calculus, W.H. Freeman & Company.
3. Robert A. Adams (2016) Calculus: A Complete Course.