## MA209-5-SP-CO:Numerical Methods

The details
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Current
Monday 13 January 2025
Friday 21 March 2025
15
22 May 2024

Requisites for this module
MA185
(none)
(none)
(none)

(none)

## Key module for

BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year)

## Module description

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.

## Module aims

The aims of this module are:

• To develop students as modern-day mathematicians, equipping them with ability to understand and solve a problem using numerical methods and appropriate software.

• To develop practical skills using software for scientific computations (Matlab or Octave), while understanding and appreciating the mathematical background and properties of algorithms they use.

## Module learning outcomes

By the end of the module, students will be expected to 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

## Module information

Indicative 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:
Classification of partial differential equations
Finite Difference Methods
Numerical stability

## Learning and teaching methods

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.

## Bibliography*

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
Coursework   Assignment 2
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period)
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment 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.

Coursework Exam
20% 80%

### Reassessment

Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Dmitry Savostyanov, email: d.savostyanov@essex.ac.uk.
Dr Dmitry Savostyanov
maths@essex.ac.uk

Availability
Yes
Yes
No

## External examiner

Prof Stephen Langdon
Brunel University London
Professor
Resources
Available via Moodle
Of 1648 hours, 20 (1.2%) hours available to students:
1628 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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