MA209-7-SP-CO:
Numerical Methods
2021/22
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 17 January 2022
Friday 25 March 2022
15
28 October 2021
Requisites for this module
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This module aims to develop students as modern-day mathematicians, equipping them with ability to understand and solve a problem using numerical methods and appropriate software. Students will develop their practical skills using software for scientific computations (Matlab or Octave), while understanding and appreciating the mathematical background and properties of algorithms they use.
On completion of the module, students should be able to:
1. Appreciate the processes and pitfalls of mathematical approximation
2. Demonstrate knowledge and understanding of the context and scope of mathematical computing
3. Motivate and describe the derivation of the numerical methods covered in the module
4. Carry out simple numerical calculations `by hand`
5. Implement algorithms in Matlab
6. Evaluate, contrast and reflect upon the numerical results arising from different algorithms
7. Appreciate, evaluate and optimise storage and computational costs required to solve a problem numerically.
1. An introduction to practical computations
2. Solving single nonlinear equations
3. Solving systems of linear equations
4. Numerical solution of ordinary differential equations
5. Interpolation of univariate functions
6. Introduction to numerical solution of partial differential equations
Syllabus
1. Programming and efficient computations in Matlab
- Factors affecting performance and numerical accuracy of the program
- Good programming practices
2. Solving single nonlinear equations
- Bisection method
- Newton-Raphson method
3. Numerical solution of ordinary differential equations
- Euler method
- Runge-Kutta methods
- Linear multi-step methods
4. Interpolation
- Polynomial interpolation
- Optimal interpolation points
5. Introduction to numerical solution of partial differential equations (specific to MA209-7)
- Classification of partial differential equations
- Finite Difference Methods
- Numerical stability
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
This module does not appear to have a published bibliography for this year.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Assignment 1 |
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| Coursework |
Assignment 2 |
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| Exam |
Main exam: 180 minutes during Summer (Main Period)
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Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Dmitry Savostyanov, email: d.savostyanov@essex.ac.uk.
Dr Dmitry Savostyanov & Dr Terry Sithole
Dr Dmitry Savostyanov (d.savostyanov@essex.ac.uk), Dr Terry Sithole (tz21720@essex.ac.uk)
Yes
No
No
Prof Stephen Langdon
Brunel University London
Professor
Available via Moodle
Of 2284 hours, 20 (0.9%) hours available to students:
2264 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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