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MATH7019 - Technological Mathematics 311

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Title:Technological Mathematics 311
Long Title:Technological Mathematics 311
Module Code:MATH7019
 
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 1 - 2015/16 ( September 2015 )
Module Delivered in 2 programme(s)
Module Coordinator: David Goulding
Module Author: Jeremiah McCarthy
Module Description: This module covers: Interpolation and curve fitting; Taylor series in one and two variables; differential equations with applications to static beams; probability distributions and statistical inference.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Find the curve of best fit to a set of data in the least squares sense.
LO2 Understand the concept of a differential equation. Solve static beam equations.
LO3 Apply Taylor Series to numerically solve differential equations and carry out error analysis.
LO4 Apply common probability distributions to engineering problems including sampling and hypothesis testing.
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).
10144 MATH6015 Technological Mathematics 2
10145 MATH6040 Technological Mathematics 201
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.
No requirements listed
Co-requisites
No Co Requisites listed
 

Module Content & Assessment

Indicative Content
Curve Fitting
Determination of a curve of best-fit to a set of data points using the method of Least Squares. Non-linear laws. Lagrange Interpolation.
Differential Equations
Review of single variable calculus. Separable first order differential equations. Step functions. Static beam equations including simply supported, fixed ends and cantilevers.
Taylor Series
Taylor Series of one variable. Euler Method and Three Term Taylor. Review of Partial Differentiation. Taylor Series of two variables. Differentials with applications to error analysis to include rounding error.
Probability & Statistics
Laws of probability. Probability distributions such as the Binomial, Poisson Distribution and Normal distributions. Applications of these distributions to engineering problems. Sampling from a Normal population. Confidence intervals for the population mean. Hypothesis tests for population means using the z-test and the t-test.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Written Report Short report utilising a software package such as Microsoft Excel to assist in fitting a curve to civil engineering data. 1 15.0 Week 5
Written Report Short report investigating an ordinary differential equation (ODE), to include utilisation of a software package such as Microsoft Excel to assist in applying Taylor methods to a perturbed ODE. 2,3 15.0 Week 10
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 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 Lecture 3.0 Every Week 3.00
Independent & Directed Learning (Non-contact) Review of lecture material, completion of exercises 4.0 Every Week 4.00
Tutorial Based on exercises 1.0 Every Week 1.00
Independent & Directed Learning (Non-contact) Review of lecture material, completion of exercises 3.0 Every Week 3.00
Total Hours 11.00
Total Weekly Learner Workload 11.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Lecture 2.0 Every Week 2.00
Tutorial Based on exercises 2.0 Every Second Week 1.00
Independent & Directed Learning (Non-contact) Review of lecture material, completion of exercies 4.0 Every Week 4.00
Total Hours 8.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 3.00
 

Module Resources

Recommended Book Resources
  • K A Stroud 2011, Advanced Engineering Mathematics, 5th Ed. [ISBN: 9780230275485]
Supplementary Book Resources
  • John Bird 2006, Higher engineering mathematics, 5th Ed., Newnes Oxford [ISBN: 9780750681520]
  • Douglas C. Montgomery, George C. Runger 2011, Applied Statistics and Probability for Engineers -Student Solution Manual 5TH EDITION, 5th Ed. [ISBN: 9780470505786]
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
CR_CCIVL_7 Bachelor of Engineering in Civil Engineering 5 Mandatory
CR_CENVI_7 Bachelor of Engineering in Environmental Engineering 5 Mandatory

Cork Institute of Technology
Rossa Avenue, Bishopstown, Cork

Tel: 021-4326100     Fax: 021-4545343
Email: help@cit.edu.ie