module specification

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

 90 hours Scheduled learning & teaching activities 210 hours Guided independent study
Assessment components
Type Weighting Qualifying mark Description
In-Course Test 25%   Test 1 (1 hour, unseen)
In-Course Test 25%   Test 2 (1 hour, unseen)
Unseen Examination 50%   Unseen Exam( 2 hours)
Running in 2024/25

(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.

None.

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.