MA209-7-SP-CO:
Numerical Methods
2019/20
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 13 January 2020
Friday 20 March 2020
15
02 January 2020
Requisites for this module
(none)
(none)
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The module introduces the students to practical techniques for carrying out numerical computations on a range of mathematical problems. Students will be expected to have an elementary acquaintance with Matlab (an introduction to Matlab will also be provided via Moodle and Lynda.com for those who need it).
On completion of the module, students should be able to:
- appreciate the processes and pitfalls of mathematical approximation
- demonstrate knowledge and understanding of mathematical computing
- motivate and describe the derivation of the numerical algorithms covered in the module
- carry out simple numerical processes “by hand”
- implement and run algorithms developed in Matlab
- evaluate, contrast and reflect upon the numerical results arising from different algorithms
- appreciate the types of partial differential equations, demonstrate knowledge and understanding of finite-difference methods, the matrix representation and numerical stability of partial differential equations
1. An introduction to practical computations
2. Solving single nonlinear equations
3. Numerical linear algebra
4. Numerical solution of ordinary differential equations
5. Simple approximation
6. Introduction to numerical solution of partial differential equations
Syllabus
1. An introduction to practical computations
- Algorithms
- Simple examples
- Pitfalls
2. Solving single nonlinear equations
- Bisection method
- Regula-Falsi method
- Newton-Raphson method
3. Numerical linear algebra
- Gaussian elimination
- Partial pivoting
- Iterative methods
4. Numerical solution of ordinary differential equations
- Euler method
- Runge-Kutta methods
- Linear multi-step methods
5. Simple approximation
- Polynomial interpolation
- Optimal interpolation points
- Fourier and trigonometric series
6. Introduction to numerical solution of partial differential equations (specific to MA209-7)
- Elliptic equations
- Parabolic equations
- Hyperbolic equations
- Finite Difference Methods
- Matric representation
- Numerical stability
The module runs at 3 hours per week except in weeks 24 and 25 in which there will be 3 and 2 additional hours (to the 3 hours per week), respectively.
1. There are two lectures and one class/laboratory each of the 10 teaching weeks (as in MA209-5).
2. There is an additional 2-hour lecture and 1-hour class/laboratory in week 10.
3. There is an additional 1-hour lecture and 1-hour class in week 11.
The additional 5 contact hours in 2. and 3. are needed to cover learning outcome 6 which is specific to MA209-7.
4. In the summer term, 3 revision lectures are given.
This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.
Assessment items, weightings and deadlines
Coursework / exam |
Description |
Deadline |
Coursework weighting |
Coursework |
Homework 1 |
10/02/2020 |
|
Coursework |
Homework 2 |
16/03/2020 |
|
Exam |
Main exam: 24hr during Summer (Main Period)
|
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
Prof Xinan Yang, email: xyangk@essex.ac.uk.
Dr Xinan Yang, email xyangk@essex.ac.uk and Dr Joe Bailey, email jbailef@essex.ac.uk
Dr Xinan Yang (xyank@essex.ac.uk)
Yes
No
No
No external examiner information available for this module.
Available via Moodle
Of 44 hours, 18 (40.9%) hours available to students:
26 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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