KL7017 - Mathematical Modelling and Simulations

What will I learn on this module?

The module covers three broad topics: 1) Ordinary differential equations, 2) eigenvalue problems, and 3) random processes. For each topic, we will explore related techniques and apply them to specific problems.

The syllabus includes:

Ordinary differential equations
Numerical methods (Euler, Runge-Kutta); phase portraits; systems of ordinary differential equations; reflection and transmission; synchronisation (entraining, Adler’s model, Arnold tongues, mutual synchronisation, nonlinear oscillators).

Eigenvalue problems
Fourier transform and series; discrete Fourier transform; asymptotic expansion; dispersion relation in periodic potentials; Bloch theorem.

Random processes
Brownian motion; Langevin equations; Ito and Stratonovich calculus; noise in Fourier space; Wiener-Khinchin theorem; Monte-Carlo integration; metropolis algorithm.

How will I learn on this module?

You will learn through lectures and practical exercises composed of seminars, coursework, and the final project. In the lectures, we will discuss the theoretical foundations for each technique and how they are applied in many different problems and scenarios. Each lecture will propose a case of study to be practically explored in the weekly seminars and practical sessions using Python or MATLAB. Practical sessions will also allow for hands-on practice in applying the concepts learned to coursework. Both coursework and the final project will require short reports to hone your presentation skills in both written and oral formats.

Formative feedback is available throughout the sessions as you learn the techniques and solve problems. We operate an open-door policy where you can meet with your module tutor to seek further advice or help if required. Summative assessment will be composed of coursework (30% of the module’s mark) and a final project (70% of the module’s mark). The coursework will be divided into three exercises, each assessed through a short, written report. The final project will explore a research question and will be assessed by a written report, an oral presentation, discussion, and critique. This means that you will be assessed on your ability to solve the problem, research literature, convey the employed techniques and main findings of your work, answer questions, and also ask questions to your classmates’ project. Both coursework and project are envisioned as group activities.

Feedback on the written reports will be given promptly. Feedback on the final presentation will be given in a specially-arranged feedback session after the end of the semester. An opportunity to discuss work further will be available on an individual basis when work is returned and also through the open door policy.

How will I be supported academically on this module?

In addition to direct contact with the module tutor during lectures, seminars and practical sessions, students are expected to approach the module tutor with questions either via email or the open-door policy operated throughout the programme. All teaching materials, selected scripts, and relevant reading material (including research articles) will be available through the e-learning portal.

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. Apply conceptual numerical techniques to solve practical problems beyond the discipline.
2. Combine several techniques to solve selected problems.

Intellectual / Professional skills & abilities:
3. Devise procedures to solve advanced problems using mathematical methods.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity):
4. Manage your own learning, through knowledge of available reading sources, including advanced texts and research papers.
5. Effectively and concisely communicate in both written and oral form.

How will I be assessed?

Coursework (50%) – 1, 2
(Assignment with set questions and problems - wordcount: max 2000 words + derivations + codes + graphs + tables + plots)

Examination (50%) – 3,4,5
(Closed book examination – 2hours, Max 2000 words + derivations + codes + tables + plots)

FORMATIVE – 1, 3, 4, 5

Formative assessment will be available during seminars through tutor-student interactions and dialogue, allowing students to extend, consolidate and evaluate their knowledge.

Formative feedback will be provided on student work by individual discussion. Solutions to seminar exercises will be provided through the e-learning portal after the students submit their solutions, allowing students to immediately verify their solutions and to seek further help from the module tutor to clarify inconsistencies





Module abstract

The pervasive use of computational techniques for data analysis makes mathematical modelling a key ability to both conduct research and increase employability. ‘Mathematical Modelling and Simulations’ will expose you to a wide range of numerical techniques for solving real-world problems. For each technique, you will learn its mathematical formulation and then apply it to solve cases of study.

The module will be based on a combination of lectures, seminars and practical computer-based seminars. Lectures give a formal introduction to the techniques’ theoretical formulation while the seminars offer the opportunity to see applications of such concepts in various problems inspired by physics and engineering as well as research conducted at the department. Practical computer-based sessions will give you the opportunity to tackle challenging problems using techniques and methods introduced in the theoretical sessions. Lectures, seminars and practical sessions will explore topics beyond the discipline, strengthening your transferable skills and employability.

Assessment will be conducted with both coursework and a final project. In the coursework, you will solve problems that require a deeper understanding of the techniques. The final project will assess your ability to apply the learned techniques for problem-solving and to present the main findings.

Course info

Credits 20

Level of Study Postgraduate

Mode of Study 1 year full-time

Department Mathematics, Physics and Electrical Engineering

Location Coach Lane Campus, Northumbria University

City Newcastle

Start September 2024

Fee Information

Module Information

All information is accurate at the time of sharing. 

Full time Courses are primarily delivered via on-campus face to face learning but could include elements of online learning. Most courses run as planned and as promoted on our website and via our marketing materials, but if there are any substantial changes (as determined by the Competition and Markets Authority) to a course or there is the potential that course may be withdrawn, we will notify all affected applicants as soon as possible with advice and guidance regarding their options. It is also important to be aware that optional modules listed on course pages may be subject to change depending on uptake numbers each year.  

Contact time is subject to increase or decrease in line with possible restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors if this is deemed necessary in future.


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