Short Title:Technical Mathematics 4
Full Title:Technical Mathematics 4
Module Code:MATH H2092
 
Credits: 5
NFQ Level:6
Field of Study:Electricity and energy
Module Delivered in 2 programme(s)
Reviewed By:JOHN ANDREW DONNELLAN
Module Author:Ciaran O Sullivan
Module Description:The first aim of Technical Mathematics 4 is to develop the students’ competence in a range of mathematical techniques in probability as applied to process capability, pattern manipulation and basic calculus in such a way as to support other engineering modules. The second aim is to deepen the students understanding of key mathematical ideas regarding the application of the normal distribution to engineering problems, sequence and the convergence of a mathematical sequence, basic integration of engineering functions (including indefinite integrals, definite integrals, and numerical integration). The third aim is to extend the students use of software applications in the processing of engineering data and understanding engineering concepts. Finally the module aims to encourage self awareness and independent learning as mathematics students through maintaining a reflective diary on their work.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Use the standard normal table to solve problems about the general normal distribution.
LO2 Construct and interpret an SPC chart.
LO3 Construct confidence intervals for means and proportions.
LO4 Recognise arithmetic and geometric sequences and calculate terms in them.
LO5 Test simple sequences for convergence or divergence and determine the limit (steady state) of simple convergent sequences
LO6 Calculate the sum of n terms in a series.
LO7 Use software tools appropriately to generate a sequence, the limit of a sequence and the sum of the first n terms of a sequence.
LO8 Use software tools appropriately to generate a series, the sum of the first n terms of a series.
LO9 Use a table of indefinite integrals and linearity to find anti-derivatives of simple functions.
LO10 Calculate definite integrals including the area under a graph.
LO11 Use the technique of substitution to integrate a composition of two functions, the first of which is linear.Use the tableau method of integration by parts and integrate rational integrands using partial fractions.
LO12 Solve a simple variable separable differential equationand solve first order linear differential equations using an integrating factor.
LO13 Use the trapezoidal rule and Simpson’s rule to approximate the value of a definite integral.
LO14 Maintain a reflective learning diary.
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) %
Probability Distributions:
The normal distribution. The standard normal table. Using the standard normal table to solve problems for general normal distributions. Confidence intervals. Statistical Process Control: X-Bar charts.
25.00%
Software skills:
Control structures (loops). Recursion (sequences and series).
13.00%
Sequences and Series:
Ordinary, explicit, and recursive forms of sequences. Arithmetic and geometric sequences. Convergence and divergence of sequences. Series as a sequence of partial sums. The ratio test.
21.00%
Integration:
Anti-derivatives of simple functions. The constant of integration. Integration of linear combinations of simple functions. Definite integrals. The area under a graph, including area below the horizontal axis. Integration of the composition of two functions, the first being a linear function. Integration using the tableau method. Integration using partial fractions. Solution of simple variable separable differential equations. Solution of first order differential equations using the integrating factor method.
29.00%
Numerical Integration:
The trapezoidal rule. Simpson’s rule.
12.00%
Assessment Breakdown%
Course Work40.00%
End of Module Formal Examination60.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Practical/Skills Evaluation High threshold ‘Key Skills’ quiz, testing key basic mathematical techniques needed for this semester. ( First opportunity to do test in week 1). 1,2,3,4,5,6,7,8,10,13 15.00 Ongoing
Continuous Assessment Written test on integration. 2,6,9,10,11,12,14 7.00 Week 8
Project Assignment on the use of SPC charts and control structures in sequences or numerical integration using appropriate software. 1,2,3,5,6,7,8,13 8.00 Week 10
Continuous Assessment Submission of Reflective Learning Diary, detailing student’s perception of how they met the learning outcomes of the syllabus. 2,6,9,10,11,12,14 10.00 Sem 2 End
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,3,4,5,6,9,10,11,12,13 60.00 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 3.00 Every Week 3.00
Lab Computer lab on use of excel and Matalb for relaiablilty, sequences and integartion, augnmented by tutorial work on problem sheet questions. Also Selected opportunities to do Keyskills tests. 1.00 Every Week 1.00
Independent Learning Review of lecture material between lectures, completion of problem sheet questions, completion of computer assignments. Reflection on and revison for Keyskills test. Synthesis of course material ahead of final semester exam. 3.00 Every Week 3.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
This module has no Part Time workload.
 

Module Resources

Required Book Resources
  • Kuldeep Singh, Palgrave, Engineering Mathematics through Applications, 1st ed Ed., Macmillan [ISBN: 0 -333– 92224 –7]
  • James Reilly,, Using Statistics, 1st ed Ed. [ISBN: 9780717140220]
Recommended Book Resources
  • 2006, CALMAT Learning Environment, CALMAT Team, 4th ed Ed., Glasgow Caledonian Uni UK
  • Tony Croft,, Foundation Maths [ISBN: 9780131979215]
  • Glyn James... [et al.], Modern engineering mathematics, Pearson Prentice Hall Harlow [ISBN: 9780132391443]
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 4 Mandatory
TA_EAEEE_D Bachelor of Engineering in Sustainable Energy & Environmental Engineering 4 Mandatory