MA5011 - Further Calculus (2020/21)
| Module specification | Module approved to run in 2020/21 | ||||||||||||||||
| 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 2020/21(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
Syllabus
− Vectors, Vector_Valued Functions
− Partial differentiation. Chain rule. Taylor series. LO1,LO2,LO3,LO4
− Maxima and minima of functions of more than one independent variable.
− Integration over plane areas. Volumes. Change of variables. Jacobians. LO2, LO5
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
Assessment strategy
Summative assessment will consist of two tests and a final examination. Test 1 will assess LO1, LO2, test 2 will assess LO2, LO3, and the final assessment will be an examination where students will be tested across the whole syllabus (LO1 to LO5).
Feedback to students will be given in class and on weblearn after the summative assessments Test1 and Test2.
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