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

Valid From: 
Semester 1  2016/17 ( September 2016 ) 
Module Delivered in 
no programmes

Module Coordinator: 
AINE NI SHE 
Module Author: 
Maryna Lishchynska 
Module Description: 
This module provides methods to visualise and compute three dimensional structures along with applying techniques of vector calculus to engineering problems. This module will give the student a broad understanding of analytical techniques for solving Partial Differential Equations. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Geometrically represent vector functions. 
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 
Classify and solve analytically second order partial differential equations . 
LO5 
Solve physical applications using 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 CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 
No recommendations listed 
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 should 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. 
Corequisites

No Co Requisites listed 
Module Content & Assessment
Indicative Content 
Vector Calculus  Multivariable Differentiation
Geometrically represent vector functions to be able to determine the tangent, arclength, curvature, velocity and acceleration. Analyse scalar and vector fields, contour maps, directional derivative and gradient vector of a scalar field, divergence and curl of a vector field.

Vector Calculus  Multivariable Integration
Line and surface integrals of scalar and vector fields and volume integrals of scalar fields. In addition, use the Divergence, Green's and Stokes' Theorems with physical applications.

Partial Differential Equations
Classify second order partial differential equations. Model and derive wave, heat and Laplace's equation. Solution of such equations by separation of variables. Solve physical applications, such as, electromagnetic wave equation, transmission line equations, electrostatic potential problems etc.

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 
10.0 
Week 4 
Short Answer Questions 
Line and Surface Integrals 
3 
10.0 
Week 8 
Short Answer Questions 
Partial Differential Equations 
4,5 
10.0 
Week 12 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,4,5 
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]
 K A Stroud, 2011, Advanced Engineering Mathematics, 5th Ed., Palgrave Macmillan [ISBN: 0230275486]
 Supplementary Book Resources 

 James Stewart, 2002, Multivariable calculus, 5th Ed., Brooks/Cole [ISBN: 0534393578]
 Anthony J. Tromba, Jerrold E. Marsden, 2003, Vector Calculus, 5th Ed., W. H. Freeman [ISBN: 1429224045]
 Howard Anton, Irl Bivens, Stephen Davis, 2012, Calculus: Late Transcendentals Single and Multivariable, 10th Ed., Wiley [ISBN: 9781118092]
 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
 