# PX276 - Methods of Mathematical Physics

• Module code: PX276
• Module name: Methods of Mathematical Physics
• Department: Physics
• Credit: 7.5

## Module content and teaching

###### Principal aims

To teach mathematical techniques needed by second, third and fourth year physics modules.

###### Principal learning outcomes

Students should be able to: Represent simple functions in terms of Fourier series and Fourier transforms; Possess a good understanding of diffraction and interference phenomena; Minimise/maximise simple functions subject to constraints using Lagrange multipliers; Express vectors in different coordinate systems, recognise some physical examples of tensors.

###### Timetabled teaching activities

20 Lectures + 10 examples classes

https://warwick.ac.uk/fac/sci/physics/current/teach/syllabi/year2/px276/

###### Other essential notes

The module starts with the theory of Fourier transforms and the Dirac delta function. Fourier transforms are used to represent functions on the whole real line using linear combinations of sines and cosines. Fourier transforms are a powerful tool in physics and applied mathematics. A Fourier transform will turn a linear differential equation with constant coefficients into a nice algebraic equation which is in general much easier to solve. The module explains why diffraction patterns in the far-field limit are the Fourier transforms of the "diffracting" object. It then looks at diffraction generally. The case of a repeated pattern of motifs illustrates beautifully one of the most important theorems in the business - the convolution theorem. The diffraction pattern is simply the product of the Fourier transform of repeated delta functions and the Fourier transform for a single copy of the motif. The module also introduces Lagrange multipliers, co-ordinate transformations and cartesian tensors illustrating them with examples of their use in physics.

## Module assessment

Assessment group Assessment name Percentage
7.5 CATS (Module code: PX276-7.5)
D1 (Assessed/examined work) Class Tests and Assessed Coursework 20%
1 hour examination (April) 80%

## Module availability

This module is available on the following courses:

###### Core
• Undergraduate Mathematics and Physics (MMathPhys) (FG31) - Year 2
• Undergraduate Mathematics and Physics (BSc MMathPhys) (FG33) - Year 2
• Undergraduate Mathematics and Physics (BSc) (GF13) - Year 2

N/A

###### Optional
• Undergraduate Mathematics (BSc) (G100) - Year 2
• Undergraduate Mathematics with Intercalated Year (G101) - Year 2
• Undergraduate Mathematics (MMath) (G103) - Year 2
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 2
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 2
• Undergraduate Mathematics and Business Studies (with Intercalated Year) (G1N2) - Year 2