Title:  Multivariable Calculus 
Long Title:  Multivariable Calculus 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2018/19 ( September 2018 ) 
Module Coordinator: 
David Goulding 
Module Author: 
Maryna Lishchynska 
Module Description: 
This module applies vector calculus and associated techniques to engineering and physics contexts. The module will also give the student an understanding of the analytical approach to solving partial differential equations relevant to engineering and physics. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Parametrise curves, differentiate vector functions and represent them geometrically. 
LO2 
Evaluate the gradient of a scalar function, the divergence and curl of a vector function. 
LO3 
Evaluate line, surface and volume integrals of scalar fields based on physical applications. 
LO4 
Analytically solve applied problems modelled by second order partial differential equations. 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).


Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

This is an advanced module. Students must have prior learning of the following topics: Differentiation; Integration; Ordinary differential equations; Basic partial differentiation. You may not enrol on this module if you have not studied these topics.
Examples of prerequisite modules: MATH6006 & MATH7006 or MATH6041 & MATH6043. 
Module Content & Assessment
Indicative Content 
Vector Calculus  Multivariable Differentiation
Geometric representation and differentiation of vector functions to determine the tangent, arclength, curvature, velocity and acceleration. Computing gradient and directional derivative of a scalar field, divergence and curl of a vector field. Using differential operators to analyse scalar and vector fields: finding a direction of heat or gas flow, investigating solenoidal/incompressible and conservative/irrotational fields.

Vector Calculus  Multivariable Integration
Line and surface integrals of scalar and vector fields and volume integrals of scalar fields with applications in chemical, electrical engineering and physics (i.e. circulation of vector field, material flux in diffusion, heat flux, electric flux). Using Divergence, Green's and Stokes' theorems with physical applications.

Partial Differential Equations
Classification of second order partial differential equations. Derivation of heat/diffusion equation, wave and Laplace's equations. Solution of such equations by separation of variables. Solving defined engineering problems specific to students' fields of study, such as heat conduction problem, diffusion problem, transmission line equation, electrostatic potential problem.

Assessment Breakdown  % 
Course Work  30.00% 
End of Module Formal Examination  70.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Short Answer Questions 
Vector calculus 
1,2 
15.0 
Week 5 
Short Answer Questions 
Line and multiple Integrals 
3 
15.0 
Week 10 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,4 
70.0 
EndofSemester 
Reassessment Requirement 
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Formal lecture 
3.0 
Every Week 
3.00 
Tutorial 
Worksheets 
1.0 
Every Week 
1.00 
Independent & Directed Learning (Noncontact) 
Review of course material 
3.0 
Every Week 
3.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
Workload: Part Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Formal lecture 
2.5 
Every Week 
2.50 
Tutorial 
Worksheets 
0.5 
Every Week 
0.50 
Independent & Directed Learning (Noncontact) 
Review of course material 
4.0 
Every Week 
4.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
3.00 
Module Resources
Recommended Book Resources 

 Erwin Kreyszig 2011, Advanced Engineering Mathematics, 10th Ed., John Wiley & Sons [ISBN: 0470646136]
 Dennis G. Zill & Warren S. Wright 2014, Advanced Engineering Mathematics, 5th Ed., Jones & Bartlett Learing USA [ISBN: 9781449691721]
 Supplementary Book Resources 

 James R. Welty, Gregory L. Rorrer, David G. Foster 2014, Fundamentals of momentum, heat and mass transfer, 6th Ed., John Wiley & Sons Hoboken N.J. [ISBN: 9781118808870]
 David S. Wilkinson 2000, Mass transport in solids and fluids, Cambridge University Press Cambridge, UK [ISBN: 0521624096]
 David K. Cheng 1989, Field and wave electromagnetics, AddisonWesley Pub. Co. Reading, Mass. [ISBN: D0201128195]
 Anthony J. Tromba & Jerrold E. Marsden 2003, Vector Calculus, 5th Ed., W. H. Freeman [ISBN: 1429224045]
 This module does not have any article/paper resources 

Other Resources 

 EBook: George Cain & James Herodhttp://people.math.gatech.edu/~cain/note
s/calculus.html
 EBook: Anil Kumar Sharmahttp://www.ebook3000.com/TextBookofVe
ctorCalculus_118051.html
 EBook: Michael Corralhttp://www.ebooksdirectory.com/details.
php?ebook=1160

Module Delivered in
