MATH7016 - Numerical Methods II

Title:Numerical Methods II
Long Title:Numerical Methods II
Module Code:MATH7016
 
Duration:1 Semester
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 1 - 2018/19 ( September 2018 )
Module Delivered in 1 programme(s)
Module Coordinator: David Goulding
Module Author: Jeremiah McCarthy
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:
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.
Pre-requisite learning
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
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.
Assessment Breakdown%
Course Work100.00%
Special Regulation
Reassessment of this module will consist of a repeat practical/written examination.
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Practical/Skills Evaluation Based on weekly 2-hour Laboratory sessions 2,5 20.0 Week 6
Short Answer Questions Mid-semester 1 hour written assessment 1,2,3 20.0 Week 7
Practical/Skills Evaluation Based on weekly 2-hour Laboratory sessions 2,4,5 20.0 Week 11
Short Answer Questions Written assessment 1,2,3,4 40.0 Week 12
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 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 Theory 2.0 Every Week 2.00
Lab Practical Lab 2.0 Every Week 2.00
Independent & Directed Learning (Non-contact) Independent learning 3.0 Every Week 3.00
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Theory 2.0 Every Week 2.00
Lab Computer practical 2.0 Every Week 2.00
Independent & Directed Learning (Non-contact) Independent learning 3.0 Every Week 3.00
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 Ed., 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