module specification

MA5011 - Further Calculus (2022/23)

Module specification Module approved to run in 2022/23
Module title Further Calculus
Module level Intermediate (05)
Credit rating for module 30
School School of Computing and Digital Media
Total study hours 300
90 hours Scheduled learning & teaching activities
210 hours Guided independent study
Assessment components
Type Weighting Qualifying mark Description
In-Course Test 25%   Test 1 (unseen)
In-Course Test 25%   Test 2 (unseen)
Unseen Examination 50%   Exam (unseen)
Running in 2022/23

(Please note that module timeslots are subject to change)
Period Campus Day Time Module Leader
Year North Friday Morning

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


− 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.


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