# KL6002 - Methods of Applied Mathematics

## What will I learn on this module?

With this module you will learn advanced methods and technical skills to find exact and approximate solutions to complex problems inspired by the real world. Examples of applications include traffic flow, waves in the ocean, optical telecommunications systems, models for climate and biological systems and magnetohydrodynamics.

Outline syllabus will develop the following three areas:

Exact methods

1) Integral transforms:
- Laplace transform,
- Fourier transform

2) Applications of integral transforms to linear differential equations.

3) Theory of quasilinear partial differential equations

4) Method of characteristics.

5) Conservation laws and shock waves.

6) Applications of exact methods to

- traffic flows
- water waves
- magnetohydrodynamics.

Asymptotic methods:

1) Asymptotic methods for algebraic equations
2) Regular and singular perturbation methods for ordinary differential equations;
3) Asymptotic methods for evaluations of integrals

Applications

1) Boundary layers
2) Linear and Nonlinear dispersive waves
3) Solitons.

### How will I learn on this module?

The module will be delivered using a combination of lectures and problem solving session, which will complement the taught material and enable you to obtain help with problems arising. In general, each topic presented in the lecture will be followed by a problem set and a problem study class. You will receive guidance on an individual basis to enhance your knowledge and expertise.

You will be assessed by written mid-term assignment (30%) a formal examination (70%) at the end of semester two. The examination will cover all aspects of the module and will assess your problem solving abilities when applied to new unseen problems.

Informal feedback on work in progress will be given continuously during the module. You will also receive formal assignment feedback at the end of the first semester and examination feedback at the end of the module.

### How will I be supported academically on this module?

Lectures and integrated problem solving sessions will be the main point of academic contact, providing you with a formal teaching environment for core learning. Outside formal scheduled teaching, you will be able to contact the module team (module tutor, year tutor, programme leader) either via email or the open door policy operated throughout the programme. Further academic support will be provided through technology-enhanced resources via the e-learning portal. You will also have the opportunity to give your feedback formally through periodic staff-student committees and directly to the module tutor at the end of the lecture.

### 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

### What will I be expected to achieve?

Knowledge & Understanding:

1. Identify suitable approaches for the analytic exact and approximate solutions of ordinary and partial differential equations and integrals.

2. Construct explicit analytic exact and approximate asymptotic solutions to Ordinary and Partial Differential equations. Derive asymptotic formulas for Integrals arising in applied problems including fluid dynamics, electrodynamics, quantum mechanics.

Intellectual / Professional skills & abilities:

3. Construct rigorous mathematical approximations and understand and control their effectiveness, and range of applicability.

4. Discuss and critically evaluate modern analytical approaches to real world problems.

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
5. Demonstrate the ability to manage time and resources effectively.

### How will I be assessed?

SUMMATIVE
1. Written assignment (30%) – 1, 3, 4, 5
Examination (70%) – 1, 2, 3, 4, 5

FORMATIVE
problem-solving classes – 1, 2, 3, 4, 5

Feedback will take several forms, including verbal feedback after lectures, individual verbal and written feedback following written assignment, and written feedback on the exam.

N/A

N/A

### Module abstract

Methods of Applied Mathematics will equip you with a broad range of advanced techniques for the exact and approximate solution of applied mathematics problems in various real-world contexts. The module will enable to identify and choose the suitable methods of mathematical approximation and will allow you to develop advanced problem-solving skills through lectures integrated with practical sessions. You will be assessed by a final examination designed to put forward your newly developed skills and techniques. You will receive constructive feedback during the formal contact hours and throughout the year. The eLearning Portal will serve as a point of contact, information and discussion with the tutor. The newly learned concepts and acquired skills will advance your knowledge of applicable mathematics and will enhance your future employability.

### Course info

UCAS Code G100

Credits 20

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 2024 or September 2025

## Mathematics BSc (Hons)

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.

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