Short Title:Technical Mathematics 5
Full Title:Technical Mathematics 5
Module Code:MATH H3073
 
Credits: 5
NFQ Level:7
Field of Study:Electricity and energy
Module Delivered in 2 programme(s)
Reviewed By:JAMES WRIGHT
Module Author:PAUL ROBINSON
Module Description:This module has two aims: 1. to introduce basic matrix techniques for the formulation and solution of engineering problems. These techniques include the representation of geometric transformations, the power method to find eigenvalues and the solution of systems of differential equations. 2. to use partial differentiation to formulate and solve optimisation problems in several variables and to perform error analysis.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Use matrices to construct and analyse geometric transformations in 2D
LO2 Find the eigenvalues of a 2 by 2 matrix
LO3 Diagonalise a 2 by 2 matrix. Find the power of a 2 by 2 matrix.
LO4 Find the largest and smallest eigenvalue of a matrix using the Power Method
LO5 Solve a system of homogeneous first order differential equations with constant coefficients (2D) using matrix techniques.
LO6 Convert a higher order DE into a system of first order DE’s
LO7 Use matrix techniques to find the normal modes and frequencies of undamped coupled oscillators
LO8 Calculate partial derivatives of polynomials and solve max/min problems in 2D
LO9 Use Lagrange multipliers to solve max/min problems.
LO10 Use partial differentiation to do error analysis
Pre-requisite learning
Co-requisite Modules
No Co-requisite modules listed
 

Module Content & Assessment

Content (The percentage workload breakdown is inidcative and subject to change) %
Linear transformations:
Representation by matrices. Dilation, projection,rotation and translation. Parametrized transformations. Inverse of a matrix. Eigenvalues and eigenvectors and their geometric interpretation.
31.00%
Linear Algebra:
Calculation of maximum and minimum eigenvalue using the Power Method for 2D and 3D matrices.
7.00%
Systems of first order ODE’s:
Review of first order and one variable ODE’s. Coupled first order DE’s – application to heat transfer. Conversion of higher order DE’s to systems of first order ones.
23.00%
Coupled second order DE’s without friction terms :
Application to coupled spring systems. Application of matrix techniques to find normal modes and frequencies.
12.00%
Applications:
Functions of more than one variable: Geometrical representation. Partial Differentiation. Higher derivatives. Optimisation for functions of several variables, Calculation of experimental error.
27.00%
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Continuous Assessment CA Test covering Linear Transformations and coupled first order differential equations 2,6,9,10 15.00 Week 7
Continuous Assessment High threshold Keyskills test and lab practical 1,2,3,4,5,6,7,8,9,10 15.00 Week 11
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4,5,6,7,8,9,10 70.00 End-of-Semester

IT Tallaght 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 Classwork 3.00 Every Week 3.00
Independent Learning Time Outside of Class 4.00 Every Week 4.00
Lecturer/Lab Session in Computing Laboratory 1.00 Every Week 1.00
Total Weekly Learner Workload 8.00
Total Weekly Contact Hours 4.00
This module has no Part Time workload.
 

Module Resources

Required Book Resources
  • K. A. Stroud, with additions by Dexter J. Booth 2007, Engineering mathematics, 4th ed Ed., Industrial Press New York [ISBN: 9780831133276]
Recommended Book Resources
  • K.A. Stroud, Dexter J. Booth, 2003, Advanced Engineering Mathematics, 4th ed Ed., Palgrave Macmillan, UK [ISBN: 9781403903129]
  • Michael E. Mortenson 2007, Geometric transformations for 3D modeling, Industrial Press New York [ISBN: 9780831133382]
This module does not have any article/paper resources
This module does not have any other resources
 

Module Delivered in

Programme Code Programme Semester Delivery
TA_EAEEE_B Bachelor of Engineering (Honours) in Sustainable Energy Engineering 5 Mandatory
TA_EAEEE_D Bachelor of Engineering in Sustainable Energy & Environmental Engineering 5 Mandatory