KD7043 - Further Mathematics for Physics

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What will I learn on this module?

This module is designed to provide the students with intellectual and professional skills in mathematics required to underpin the study of physics at level 7 (beyond BSc level). Hands-on training in mathematical techniques to model physical phenomena in this module is aimed at enhancing students’ employability and/or potential engagement in doctoral training.

The mathematical techniques covered include series solutions to ordinary differential equations, integral methods and solutions to inhomogeneous ordinary and partial differential equations, and calculus of variations. The module will also introduce students to advanced modeling techniques using specialist software, such as Matlab and Mathematica.

I. Series solutions of ordinary differential equations. Legendre polynomials, Bessel functions, sets of orthogonal functions.

II. Integral methods for ordinary and partial differential equations. Green’s functions, application to solutions of differential equations.

III. Calculus of variations. Functionals, variations and functional derivatives, extrema, Euler-Lagrange equations.

IV. Advanced computer-assisted modelling. Formulation and solution of mathematical problems linked to parts I-III using specialist software, such as Matlab and Mathematica.

How will I learn on this module?

The learning strategy of this module is based on a combination of lectures and seminars. Lectures give a formal introduction to physical and mathematical aspects to be applied in seminars. Seminars will be used to discuss and analyse research-led problems both analytically and numerically using computer-assisted calculations. Problems will be set out in advance of seminars. The combination of tutor-directed learning and

The student will develop skills in the use of further mathematical techniques to solve a selection of problems in physics directly linked to the content delivered in other modules of the MPhys in Physics programme (EE0728 and EE0729) or the MPhys in Physics with Astrophysics programme (EE0728 and EE0731).

Assessment will be through coursework (20%) and formal examination (80%). Exam feedback will be provided both individually and generically to indicate where the cohort has a stronger or weaker answer to examination questions. Written feedback will be provided on the coursework. Formative feedback will be provided during seminars.

Independent study is supported by further technology-enhanced resources provided via the e-learning portal, including lecture notes, e-hand outs, sample problems and past-paper questions.

How will I be supported academically on this module?

Lectures and seminars will be the main point of academic contact, offering the student with a formal teaching environment for core learning. Seminars will provide students with opportunities for critical enquiry and exchanges.

Outside formal scheduled teaching, students 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. Students will have the opportunity to give their feedback formally through periodic staff-student committees and directly to the module tutor at the end of the semester.

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:
• Apply mathematical techniques beyond BSc level to formulate and tackle Physics problems.
Intellectual / Professional skills & abilities:
• Analyse and solve ordinary and partial differential equations using integral methods.
• Formulate and analyse multivariate problems using calculus of variations.
• Formulate and analyse mathematical problems using computer-assisted tools, such as Matlab and Mathematica.
Personal Values Attributes (Global / Cultural awareness, Ethics, Curiosity) (PVA):
• Perform critical evaluation and comparisons of mathematical models to represent physical phenomena.

How will I be assessed?

SUMMATIVE
1. Coursework (20%) – KU1, ISA1, ISA2, ISA3, PVA1
2. Exam (80%) – KU1, ISA1-ISA3, PVA1

FORMATIVE
1. Seminars KU1, ISA1, ISA2, ISA3, PVA1

Feedback will take several forms including: individual verbal / written comments on work delivered in class or via blackboard; verbal feedback on the seminar work; written feedback on the assignment.

Pre-requisite(s)

N/A

Co-requisite(s)

N/A

Module abstract

This module is designed to provide you with advanced skills in mathematics required to underpin the study of research-level problems in Physics. Through lectures and seminars, you will learn mathematical techniques including integral methods and solutions to inhomogeneous ordinary and partial differential equations and calculus of variations. The module will also introduce you to advanced modeling techniques using specialist software, such as Matlab and Mathematica, and facilities, such as a high-spec computational cluster. Summative assessment will be in the form of a marked problem set (20%) and a closed-book exam (80%). This module will equip you with mathematical techniques used to model physical phenomena enhancing your employability and/or potential engagement in doctoral training.

Course info

UCAS Code F301

Credits 20

Level of Study Undergraduate

Mode of Study 4 years full-time or 5 years with a placement (sandwich)/study abroad

Department Mathematics, Physics and Electrical Engineering

Location City Campus, Northumbria University

City Newcastle

Start September 2020

Fee Information

Module Information

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