What will I learn on this module?
The module is designed to introduce you to a first mathematical treatment of ordinary and partial differential equations. You will learn fundamental techniques for solving first- and second-order equations as well as approximation methods. These are used to explore the question of the existence of solutions and provide a qualitative behaviour of the solutions. Examples are drawn from applications to physics, engineering, biology, economics and finance and modelling of complex systems.
The module will cover topics such as:
Ordinary Differential Equations (ODEs)
1. First-order ODEs: Classification of ODEs, separable, Bernoulli, Riccati and exact equations as well as integrating factors. Picard iterations and existence of solutions.
2. Second-order ODEs: Solutions of linear equations, independence of solutions, linear stability, initial and boundary value problems, series solutions about ordinary and singular points, special functions
Partial Differential Equations (PDEs)
1. Introduction and classification of PDEs.
2. Method of characteristics for first order linear PDEs.
3. The method of separation of variables and Fourier series.
4. Solutions of Laplace, diffusion/heat and wave equations.
5. Applications
How will I learn on this module?
You will learn through a combination of lectures and skills periods focussing on problem solving where you will be able to obtain help. Lectures allow students to experience and understand the formalism of the required mathematical techniques as well as include relevant examples and guided in-class exercise-solving sessions between more theoretical expositions. Students have an opportunity to enhance their understanding of the subject through seminars which promote both independent learning and problem solving within peer groups. The seminars will also be an opportunity to present you with open research problems, and will strengthen your transferable skills and employability. Northumbria’s computer labs and facilities are fully equipped with the latest industry-standard software such as Matlab and the computer algebra system Mathematica which will be used to support independent study and learning. Further technology-enhanced resources such as e-lecture notes, seminar sheets with answers and solution and past-paper questions will be provided via the e-learning portal.
How will I be supported academically on this module?
In addition to academic 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. Students will also be regularly referred to supporting resources including relevant texts and relevant multimedia materials. References to these resources will be made available through the e-learning portal and in lectures and seminars.
You will be assessed by a coursework and a formal examination (30% and 70%, respectively). The examinations will cover all topics from the module. Formative feedback will be provided on seminar work which will include problems designed to aid your understanding.
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. Online reading lists (provided after enrolment) give you access to your reading material for your modules. The Library works in partnership with your module tutors to ensure you have access to the material that you need.
What will I be expected to achieve?
Knowledge & Understanding:
1. Apply fundamental techniques for solving ODEs about ordinary and singular points.
2. Apply the method of separation of variables and Fourier series to the Laplace, heat/diffusion and wave equations.
Intellectual / Professional skills & abilities:
3. Apply ODEs, PDEs and computer algebra to model and provide a comprehensive solution to applied problems.
Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
4. Demonstrate critical enquiry and the ability to learn independently (see PVA1 from Programme Learning Outcomes).
5. Manifest the ability to contribute to discussions and to communicate new knowledge and research findings in mathematics and statistics (see PVA3 from Programme Learning Outcomes).
How will I be assessed?
SUMMATIVE
1. Coursework (30%) – 1, 3, 4, 5
2. Examination (70%) – 1, 2, 3, 4, 5
FORMATIVE
Seminars – 1, 2, 3, 4, 5
Students will be assessed by a coursework and a formal examination (30% and 70%, respectively).
Formative feedback will be provided on seminar work which will include problems designed to aid student understanding.
Pre-requisite(s)
None
Co-requisite(s)
None
Module abstract
The study of ordinary and partial differential equations is a central theme in mathematics since it represents a cornerstone which takes advantage of your abilities from more pure topics to provide you with indispensable tools to tackle equations arising from research problems in engineering, physics, life sciences and many branches of mathematics. The topic requires a dual approach, both during the lectures and the tutorials, which combines theoretical and computational aspects and prepares you for more concrete subjects as well as more advanced ones. The module dynamically employs state-of-the-art computer algebra software to complement your analytical skills as well as obtain a visual glimpse of the solutions and their geometry. You will be assessed by a coursework and a formal examination (30% and 70%, respectively). The examinations will cover all topics from the module. Formative feedback will be provided on seminar work which will include problems designed to aid your understanding.
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 2025
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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