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MATH8010 - Multivariable Calculus

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Title:Multivariable Calculus
Long Title:Multivariable Calculus
Module Code:MATH8010
 
Credits: 5
NFQ Level:Advanced
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.
Pre-requisite 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
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 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.
Co-requisites
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 Work30.00%
End of Module Formal Examination70.00%
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 End-of-Semester Final Examination 1,2,3,4,5 70.0 End-of-Semester
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 (Non-contact) 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 (Non-contact) 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: 978-1-118-092]
This module does not have any article/paper resources
Other Resources
  • E-Book: George Cain & James Herodhttp://people.math.gatech.edu/~cain/note s/calculus.html
  • E-Book: Anil Kumar Sharmahttp://www.ebook3000.com/Text-Book-of-Ve ctor-Calculus_118051.html
  • E-Book: Michael Corralhttp://www.e-booksdirectory.com/details. php?ebook=1160
 

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