KC4012 - Computational Mathematics

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What will I learn on this module?

Mathematics students require knowledge of a range of computational tools to complement their mathematical skills. You will be using MATLAB, an interactive programming environment that uses high-level language to solve mathematics and visualise data. In addition, you will be investigating the development of algorithms through a selection of mathematical problems. Elements of the MATLAB language will be integrated throughout with various methods and techniques from numerical mathematics such as interpolation, numerical solution of differential equations, numerical solution of non-linear equations and numerical integration.

The computer skills you will become conversant with include programming concepts such as the use of variables, assignments,
expressions, scriptfiles, functions, conditionals, loops, input and output. You will be applying MATLAB to solve mathematical problems and display results appropriately.

The range of numerical techniques that will be covered will include a selection from the following topics:
• Solution of non-linear equations by bisection, fixed-point iteration and Newton-Raphson methods.
• Interpolation using linear, least squares and Lagrange polynomial methods.
• Numerical differentiation.
• Numerical integration using trapezoidal and Simpson quadrature formulae.
• Numerical solution of Ordinary Differential Equations using Euler and Taylor methods for first-order initial value problems.
• Numerical solution of systems of linear equations using elementary methods.

How will I learn on this module?

You will learn through a combination of lectures and computer laboratory sessions. You will become fluent in the concepts and numerical techniques that are introduced in the lectures by attending hands-on sessions in Northumbria’s computer laboratories, during which you will work through problems to develop your knowledge and skills using MATLAB and with the support of a tutor.

How will I be supported academically on this module?

Support will include feedback from tutors during small-group computer laboratory sessions. In addition to direct contact with the module team during lectures and seminars, students are encouraged to develop their curiosity by making direct contact with the module team either via email or the open door policy operated throughout the programme. Supporting material will be placed on the e-learning portal of the university.

What will I be expected to read on this module?

All modules at Northumbria include a range of reading materials that students are expected to engage with. The reading list for this module can be found at: http://readinglists.northumbria.ac.uk
(Reading List service online guide for academic staff this containing contact details for the Reading List team – http://library.northumbria.ac.uk/readinglists)

What will I be expected to achieve?

Knowledge & Understanding:
1. You will be able to demonstrate a familiarity with MATLAB by using, reading, adapting, writing and implementing MATLAB programs.
2. You will be able to derive and apply a range of numerical methods for solving mathematical problems.

Intellectual / Professional skills & abilities:
3. You will be able to select appropriate computational methods to solve mathematical problems and to tabulate, manipulate and plot data.
4. You will recognise the limitations of available computational techniques in terms of their applicability and accuracy.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. You will be able to demonstrate essential information technology skills using professional software.

How will I be assessed?

SUMMATIVE
1. In-class test (20%) – 1, 3
2. Examination (80%) – 1, 2, 3, 4, 5

FORMATIVE
Seminar problems – 1, 2, 3, 4, 5

Assessment is by means of an in-class test (30%) and a final laboratory based examination (70%). Both assessments will be practically orientated, designed to reinforce your learning experience and to provide evidence of your level of attainment.

Summative feedback will be given directly after the coursework and the exam. You will also receive formative feedback throughout the course, in particular during the problem-solving computer laboratory sessions.

Pre-requisite(s)

None

Co-requisite(s)

None

Module abstract

‘Computational Mathematics’ will enable you to solve mathematical problems through numerical techniques using the interactive programming environment MATLAB. You will be investigating the development of algorithms and derive numerical methods to solve mathematical problems that prove intractable using an analytical approach.

‘Computational Mathematics’ follows a practical approach, with lectures supported by regular sessions in Northumbria University’s computer laboratories, during which you will work through problems to develop your knowledge and skills using MATLAB with the support of a tutor. You will be assessed by an in-class test (30%) as well as a final examination (70%), both of which will be practically orientated in order to bring together all your new skills and techniques.

You will enhance your employability through ‘Computational Mathematics’, enabling you to demonstrate a combination of computational and mathematical skills that are highly prized by businesses in our modern economy and are directly relevant to further study.

What will I learn on this module?

Mathematics students require knowledge of a range of computational tools to complement their mathematical skills. You will be using MATLAB, an interactive programming environment that uses high-level language to solve mathematics and visualise data. In addition, you will be investigating the development of algorithms through a selection of mathematical problems. Elements of the MATLAB language will be integrated throughout with various methods and techniques from numerical mathematics such as interpolation, numerical solution of differential equations, numerical solution of non-linear equations and numerical integration.

The computer skills you will become conversant with include programming concepts such as the use of variables, assignments,
expressions, scriptfiles, functions, conditionals, loops, input and output. You will be applying MATLAB to solve mathematical problems and display results appropriately.

The range of numerical techniques that will be covered will include a selection from the following topics:
• Solution of non-linear equations by bisection, fixed-point iteration and Newton-Raphson methods.
• Interpolation using linear, least squares and Lagrange polynomial methods.
• Numerical differentiation.
• Numerical integration using trapezoidal and Simpson quadrature formulae.
• Numerical solution of Ordinary Differential Equations using Euler and Taylor methods for first-order initial value problems.
• Numerical solution of systems of linear equations using elementary methods.

Course info

UCAS Code G100

Credits 20

Level of Study Undergraduate

Mode of Study 3 years full-time or 4 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020

Fee Information

Module Information

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