Short Title:Mathematical Methods
Full Title:Mathematical Methods
Language of Instruction:English
Module Code:MATH H4000
 
Credits: 5
NFQ Level:8
Field of Study:Mechanics and metal work
Module Delivered in 2 programme(s)
Reviewed By:DIARMUID RUSH
Module Author:NOEL GORMAN
Module Description:This module aims to equip students with the calculus and linear algebra based mathematical methods needed in the analysis of many engineering systems
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Use Taylor’s Theorem and Maclaurin series to construct approximation schemes.
LO2 Test a power series for convergence using the Ratio Test.
LO3 Calculate derivatives implicitly and partial derivatives with the nabla operator.
LO4 Calculate single integrals by reduction formulas and multiple integrals by changing variables.
LO5 Use integral transform methods to solve ordinary and partial differential equations occurring in engineering.
LO6 Apply the algebra of matrices to engineering applications.
LO7 Relate the concepts of matrices and vectors in both geometric and algebraic applications.
LO8 Solve dense and tridiagonal systems of equations occurring in engineering modelling directly.
LO9 Solve sparse systems of equations occurring in engineering modelling using efficient iterative methods.
LO10 Recognise the importance of conditioning and sensitivity in the use of Linear Algebra in the solution of real engineering models using computers.
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) %
Limits and Series.
Properties of limits. Differentiability. Implicit differentiation. Derivative of an inverse function. Taylor’s theorem. Maclaurin series. Application to approximation schemes for solving non-linear equations and calculating integrals. Convergence of power series and the Ratio Test. Integration by parts. Reduction formulas. The Gamma function.
20.00%
Calculus of Several Variables
Chain rule for partial derivatives. Cylindrical and spherical polar coordinates. Directional derivative. The nabla operator. Calculation of gradient of a scalar field and divergence and curl of a vector field. Double and Triple integrals. Change of variables.
25.00%
Laplace Transforms
Review of Laplace transform solution of second-order linear differential equations, and systems of first-order differential equations, with constant coefficients. Applications to engineering systems. Solution of classical partial differential equations by separation of variables. Laplace transform solution of partial differential equations occurring in engineering.
20.00%
Vectors
Vectors in two and three dimensions. Geometric interpretation. Norm of a vector. Dot Product. Lines and planes. Extension to higher dimensions.
5.00%
Vector spaces.
Definition of a Vector Space. Basis. Dimension. Spanning set. Linear independence.
5.00%
Inner Products
Inner products. Norms. Orthogonality. Inner product spaces.
5.00%
Linear Transformations
Definition of a Linear Transformation. Rotations in 2D and 3D. Kernel and Range. Matrices as Linear Transformations. The four fundamental subspaces.
5.00%
Matrices
Matrices. Revision of matrix algebra. Classes of matrices. Inverse of a matrix. Determinants.
5.00%
Systems of Equations
Systems of Equations. Partial pivoting. Gaussian Elimination in the context of LU Decomposition, Thomas Algorithm. Uniqueness of solutions.
5.00%
Numerical Linear Algebra
Condition of a matrix. Iterative methods for sparse systems: Jacobi, Gauss-Seidel, SOR.
5.00%
Assessment Breakdown%
Course Work20.00%
End of Module Formal Examination80.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Continuous Assessment In class tests in calculus methods and linear algebra. 1,2,3,6,7,8 20.00 n/a
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 80.00 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.

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 No Description 6.00 Every Week 6.00
Independent Learning Time No Description 4.00 Every Week 4.00
Total Weekly Learner Workload 10.00
Total Weekly Contact Hours 6.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture 4 4.00 Every Week 4.00
Independent Learning 3 3.00 Every Week 3.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 

Module Resources

Required Book Resources
  • Course Notes
Recommended Book Resources
  • Erwin Kreyszig 2011, Advanced Engineering Mathematics, 10th Ed. Ed., John Wiley & Sons [ISBN: 978-047064613]
  • K A Stroud 2011, Advanced Engineering Mathematics, 7th Ed. Ed., Palgrave Macmillan [ISBN: 978-023027548]
  • Glyn James, David Burley, Dick Clements, Phil Dyke, John Searl 2010, Advanced Modern Engineering Mathematics, Prentice Hall [ISBN: 978-0273719236]
  • Gilbert Strang, Introduction to Linear Algebra, 10th ed. Ed., Wellesley Cambridge Pr [ISBN: 9780980232714]
  • Gilbert Strang 2006, Linear algebra and its applications, Thomson Brooks/Cole Belmont, Calif. [ISBN: 978-0030105678]
  • Howard Anton, Robert C. Busby 2003, Contemporary linear algebra, Wiley New York [ISBN: 0471163627]
  • Howard Anton, Chris Rorres, Elementary Linear Algebra with Supplemental Applications, Wiley [ISBN: 978-0470561577]
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_EMECH_B B.Eng (Honours) in Mechanical Engineering [1 year Add-On] 7 Mandatory
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 7 Mandatory