Course Details in 2022/23 Session

Module Title	LI Mathematics for Physicists 2A
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	03 34465
Module Lead	Professor Mike Gunn & Professor Igor V Lerner
Level	Intermediate Level
Credits	10
Semester	Semester 1
Pre-requisites	LC Mathematics for Physicists 1A - (03 34459) LC Mathematics for Physicists 1B - (03 34462)
Co-requisites
Restrictions	None
Contact Hours	Lecture-33 hours Practical Classes and workshops-11 hours Guided independent study-56 hours Total: 100 hours
Exclusions
Description	Mathematics is the natural language in which to express physics problems, and it is therefore important that any working physicist should be fluent in it. This module is the last compulsory mathematics module in all except theory programmes, and contains the remaining core mathematics needed for all physics modules in future years. The course is delivered in two linked 10-credit modules divided into two parts: Calculus (approx. 15 credits) & Matrices and Linear Algebra (approx. 5 credits). These are further sub-divided as shown below: 1. Calculus: Vector Calculus Distributions Fourier Series Fourier Transforms Partial Differential Equations 2. Matrices and Linear Algebra: Basic Matrix Algebra Eigenvalues and Eigenvectors Most of the equations encountered in physics are linear partial differential equations (PDEs), and the calculus section is focussed on the techniques needed to formulate and solve these equations, using examples from physics. Vector calculus is the language in which both the Maxwell equations of electromagnetism, and the Navier-Stokes equation of fluid mechanics are written; the Laplacian derived in vector calculus is also at the heart of most PDEs found in physics. Fourier series and Fourier transforms involve splitting periodic and non-periodic functions respectively into their frequency components. They are extensively used in many areas of physics, including optics and wave phenomena, classical mechanics, and quantum mechanics. Finally, the section on PDEs introduces the method of separation of variables, which reduces a PDE to a set of ordinary differential equations (ODEs); the solution of such ODEs is largely beyond the scope of this module, and is a main part of the Eigenphysics module. Matrices arise in the analysis of many physical situations; examples include moments of inertia in rigid bodies, normal modes in coupled oscillators, Lorentz transformations in special relativity, and perturbation theory in quantum mechanics. In this module the properties of matrices are developed from basic algebra to thesolution of eigenvalue problems, using appropriate examples from physics.
Learning Outcomes	By the end of the module students should be able to: Calculate the gradient, divergence, curl, and Laplacian in cartesian or other orthogonal coordinate systems. Prove the standard vector calculus identities. Test a coordinate system to see if it is orthogonal. Evaluate line, surface and volume integrals. State the divergence and Stokes theorems, and verify them in a particular situation. Define and use Heaviside and Dirac delta functions, including delta functions of non-trivial argument. Derive the formulae for real and complex Fourier series, including Parseval’s theorem. Represent a given periodic function as a Fourier series. Write down the formulae for Fourier transform, inverse Fourier transform and Parseval’s theorem. Write down the formulae for Fourier sine and cosine transforms, and higher dimensional Fourier transforms. Evaluate the Fourier transform of simple functions. Explain the role of the Fourier transform in Fraunhofer diffraction, and use it to evaluate diffraction patterns.
Assessment	34465-01 : Examination : Exam (Centrally Timetabled) - Written Unseen (80%) 34465-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions	Class Test (20%); 1.5 hours Examination (80%)
Other
Reading List