Short Title:Mathematics 4
Full Title:Mathematics 4
Module Code:MATH H2005
 
Credits: 5
NFQ Level:8
Field of Study:Mechanics and metal work
Module Delivered in 2 programme(s)
Reviewed By:FIONA CRANLEY
Module Author:CIARAN TAYLOR
Module Description:The first aim of Mathematics 4 is to further develop the broad range of standard mathematical techniques in linear algebra, analysis and calculus assimilated in Mathematics 2. The second aim is to enable the student to apply these mathematical techniques to the solution of bounded engineering problems.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Find partial derivatives of functions of several variables.
LO2 Use partial derivatives to find the gradient of a scalar field and the divergence and curl of a vector field. [POa, POb, POd, POg]
LO3 Obtain definite and indefinite integrals of functions using standard integration methods. [POa, POb]
LO4 Apply integration methods to solving engineering problems. [POa, POb,POd]
LO5 Obtain eigenvalues and eigenvectors of 2 × 2 and simple 3 × 3 matrices. [POa, POb, POd]
LO6 Solve non-linear equations using appropriate techniques and software and to understand their limitations. [POa, POb, POd]
Pre-requisite learning
Co-requisite Modules
2234MATH H1018Mathematics 1
2750MATH H1019Mathematics 2
 

Module Content & Assessment

Content (The percentage workload breakdown is inidcative and subject to change) %
Introduction to functions of several variables: (6 hrs)
Evaluation of functions of several variables. Plotting. Partial differentiation. Vector fields. Divergence and curl of a vector Field.
12.00%
Vector Calculus
Scalar fields, vector fields. Calculate the gradient of a scalar field and the divergence and curl of a vector field.
19.00%
Integration: (13 hrs)
Integration methods: Definite and Indefinite Using substitution. Further Substitutions. Integration by Parts. Improper Integrals. Partial fractions
25.00%
Applications (9 hrs)
Applications of integration: Solving practical problems using integration.
17.00%
Eigenvalues and Eigenvectors: (6 hrs)
Eigenvectors and Eigenvalues
12.00%
Solution of Non Linear Equations: (8 hrs)
Graphical exploration to locate approximate roots. Iterative point estimation and interval reduction methods. Convergence of iterative methods. Use of appropriate software to solve non-linear equations.
15.00%
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other Assignment in the visualization of functions in 3-D using appropriate software and the use symbolic of mathematics software. (Using for example MATLAB).   10.00 Week 4
Other High threshold test in methods and application of integral calculus and sequences and series.   10.00 Week 7
Other Assignment in the application of point estimation and interval reduction methods to the solution of non-linear equations. (Using for example Excel/MATLAB).   10.00 Week 10
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination   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 No Description 3.00 Every Week 3.00
Lab Computer packages, problem solving 1.00 Every Week 1.00
Independent Learning No Description 4.00 Every Week 4.00
Total Weekly Learner Workload 8.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture No Description 2.00 Every Week 2.00
Lab Computer packages, problem solving 5.00 Week 13 0.38
Independent Learning Time No Description 6.00 Every Week 6.00
Total Weekly Learner Workload 8.38
Total Weekly Contact Hours 2.38
 

Module Resources

Required Book Resources
  • Glyn James... [et al.] 2001, Modern engineering mathematics, Prentice Hall [ISBN: ISBN: 0130183199]
Recommended Book Resources
  • Howard Anton, Chris Rorres 2000, Elementary linear algebra, Wiley New York [ISBN: ISBN: 0471170526]
  • H Anton 2002, Contemporary Linear Algebra MATLAB Technology Resource Manual, John Wiley and Sons
  • K. A. Stroud; with additions by Dexter J. Booth 2001, Engineering mathematics, Palgrave Basingstoke [ISBN: ISBN: 0333919394]
  • Anthony Croft, Robert Davison, Martin Hargreaves 2000, Engineering mathematics, A Foundation for Electronic, Electrical, Communications and Systems Engineers, Prentice Hall [ISBN: ISBN 0130268585]
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_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 4 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 4 Mandatory