Module Details

Module Code: MATH8010
Title: Multivariable Calculus
Long Title: Multivariable Calculus
NFQ Level: Advanced
Valid From: Semester 1 - 2018/19 ( September 2018 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 3 programme(s)
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:
# Learning Outcome Description
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.
Dependencies
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
Co-requisite Modules
No Co-requisite 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 pre-requisite modules: MATH6006 & MATH7006 or MATH6041 & MATH6043.
 
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.
Module Content & Assessment
Assessment Breakdown%
Coursework30.00%
End of Module Formal Examination70.00%

Assessments

Coursework
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 5 Learning Outcomes 1,2
Assessment Description
Vector calculus
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 10 Learning Outcomes 3
Assessment Description
Line and multiple Integrals
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 70
Timing End-of-Semester Learning Outcomes 1,2,3,4
Assessment Description
End-of-Semester Final Examination
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 University reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal lecture Every Week 3.00 3
Tutorial Contact Worksheets Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Review of course material Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal lecture Every Week 2.50 2.5
Tutorial Contact Worksheets Every Week 0.50 0.5
Independent & Directed Learning (Non-contact) Non Contact Review of course material Every Week 4.00 4
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. John Wiley & Sons, [ISBN: 0470646136].
  • Dennis G. Zill & Warren S. Wright. (2014), Advanced Engineering Mathematics, 5th. 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. 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, Addison-Wesley Pub. Co., Reading, Mass., [ISBN: D0201128195].
  • Anthony J. Tromba & Jerrold E. Marsden. (2003), Vector Calculus, 5th. W. H. Freeman, [ISBN: 1429224045].
This module does not have any article/paper resources
Other Resources
  • E-Book, George Cain & James Herod. http://people.math.gatech.edu/~cain/note s/calculus.html.
  • E-Book, Anil Kumar Sharma. http://www.ebook3000.com/Text-Book-of-Ve ctor-Calculus_118051.html.
  • E-Book, Michael Corral. http://www.e-booksdirectory.com/details. php?ebook=1160.
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_ECPEN_8 Bachelor of Engineering (Honours) in Chemical and Biopharmaceutical Engineering 8 Elective
CR_EEPSY_8 Bachelor of Engineering (Honours) in Electrical Engineering 8 Elective
CR_EELES_8 Bachelor of Engineering (Honours) in Electronic Engineering 8 Elective