KC5008 - Ordinary & Partial Differential Equations

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.

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.

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.

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).

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.

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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.