KL5002 - Further Mathematics

The module will be delivered using a combination of lectures and seminars using exercises in which students will be able to obtain help with difficulties arising. The emphasis will be that lectures formally introduce and present theories. Seminars will encourage small group-based, student-led exercises, which include working with classmates, guidance from tutor to develop and consolidate understanding. The outcomes of these student-led sessions will be disseminated to the class via the eLP course site in order to facilitate your independent learning. Independent learning also involves in reading ahead of the lectures and preparing for the seminars.

You will receive continuous feedback and guidance, which will be a fundamental underpinning principle in both classroom sessions and seminars. You will be encouraged to feedback to tutors following such reflective activities to enable them to monitor progress and develop in-class strategies to provide further support if required. In addition, you will receive written/typed/verbal feedback in response to your summative assessment submissions. The eLP will be used throughout this module to support your learning. It will accommodate many electronically-based learning resources that will enhance your learning experience.

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)

Knowledge & Understanding:
1. Formulate and solve linear matrix equations
2. Solve algebraic eigenvalue problems, do sensitivity analysis of eigenvalues and eigenvectors
3. Understand and use the techniques for the formulation and solution of certain standard, commonly occurring boundary value problems
4. Understand the fundamentals of analytical expansion techniques, such as Rayleigh-Ritz, Galerkin, finite elements, serving for approximate solution of partial differential equations.

Intellectual / Professional skills & abilities:
5. Practical skills of implementation of finite difference and finite element methods for the formulation and solution of simple problems in engineering analysis

Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
6. Develop curiosity, creativity and initiative when dealing with standard and non-standard civil engineering problems.

Summative assessment and rationale for tasks

001 Test (An open book in-class test, MLO 1):

The class test will be organized by the module team and will require you to demonstrate the use of Gauss elimination method to solve systems of linear equations and ability to interpret solutions written in parametric vector form.

002 Examination: (A closed book examination, MLO 1 to 5).

The final examination will require you to demonstrate the skills in inverting matrices using Gauss-Jordan algorithm, understanding the Rank Theorem, finding eigenvalues and eigenvectors, solving systems of ordinary differential equations (ODEs), solving initial-value problems and boundary value problems (BVPs) for ODEs, understanding variational principles, solving constrained optimization problems, understanding and using Galerkin and Finite Element Method for approximates solution of BVPs and boundary eigenvalue problems for ODEs.


Tutorial sessions will encourage the students to identify and explore areas of learning to support their progression through the module.

Indication of how students will get feedback and how this will support their learning

The in-class test feedback will be provided via the module electronic portal site addressing generic consideration of the students’ work. Individual feedback will be provided to the test submissions to clarify points of learning that have not been fully assimilated.

Tutorial sessions will provide a forum for the formative delivery of feedback on individual student progression.
Feedback from the examination will be presented on the e-learning portal.

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This module is designed to further develop your expertise in engineering mathematics, which becomes very important for your programme and future career path. Through a research-rich content which is delivered by analytical problem solving, this module will provide the student to solve challenging problems in later years of Civil Engineering degree. The contents will include practical and real life problems from a wide range of engineering applications to show the relevance of the various mathematical tools. Teaching methods will include lectures and tutorials where students can interact among themselves as well as with the tutors. Regular feedback on their learning will be provided during seminars and formal feedback through the in-class test and final assessment.