MATH7016 - Numerical Methods II

Module Details

Module Code: MATH7016
Title: Numerical Methods II
Long Title: Numerical Methods II
NFQ Level: Intermediate
Valid From: Semester 1 - 2018/19 ( September 2018 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 1 programme(s)
Module Description: This module introduces the student to numerical methods used in the study of both ordinary and partial differential equations.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Explain the need for numerical methods in the study of differential equations that arise in engineering problems.
LO2 Obtain approximate solutions to ordinary differential equations with initial/boundary conditions.
LO3 Understand the presence and challenge of error in numerical methods.
LO4 Employ finite differences to approximate partial differential equations, including Laplace's Equation and the Heat Equation.
LO5 Use an appropriate programming language to implement given algorithms.
Dependencies
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 MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
10157 MATH6031 Engineering Computing 1
10158 MATH7015 Numerical Methods 1
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
 
Indicative Content
First Order Problems
Taylor Series. Euler Method. Three Term Taylor Method. Heun's Method. Runge-Kutta Methods. Error.
Second Order Problems
Systems of Equations and higher-order equations. Boundary value problems. The Shooting Method. Finite Differences. Error.
2D Laplace's Equation
Finite differences. Relaxation Methods. Mean Value Property. Derivative and irregular boundary. Convergence.
1D Heat Equation
Implicit and Explicit Finite Differences. Stability and Convergence.
Module Content & Assessment
Assessment Breakdown%
Coursework100.00%
Special Regulation
Reassessment of this module will consist of a repeat practical/written examination.

Assessments

Coursework
Assessment Type Practical/Skills Evaluation % of Total Mark 20
Timing Week 6 Learning Outcomes 2,5
Assessment Description
Based on weekly 2-hour Laboratory sessions
Assessment Type Short Answer Questions % of Total Mark 20
Timing Week 7 Learning Outcomes 1,2,3
Assessment Description
Mid-semester 1 hour written assessment
Assessment Type Practical/Skills Evaluation % of Total Mark 20
Timing Week 11 Learning Outcomes 2,4,5
Assessment Description
Based on weekly 2-hour Laboratory sessions
Assessment Type Short Answer Questions % of Total Mark 40
Timing Week 12 Learning Outcomes 1,2,3,4
Assessment Description
Written assessment
No End of Module Formal Examination
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 University reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Theory Every Week 2.00 2
Lab Contact Practical Lab Every Week 2.00 2
Independent & Directed Learning (Non-contact) Non Contact Independent learning Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Theory Every Week 2.00 2
Lab Contact Computer practical Every Week 2.00 2
Independent & Directed Learning (Non-contact) Non Contact Independent learning Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 
Module Resources
Recommended Book Resources
  • S.C. Chapra, R. P. Canale. (2015), Numerical Methods for Engineers, 7th. McGraw-Hill Higher Education, [ISBN: 978-007340106].
  • J. Walkenbach. (2010), Microsoft Excel 2010: Power Programming with VBA, Wiley, [ISBN: 978-047047535].
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_EMECH_8 Bachelor of Engineering (Honours) in Mechanical Engineering 4 Mandatory