Course Details in 2022/23 Session

Module Title	LI Mathematics for Physicists 2B
School	Physics and Astronomy
Department	Physics & Astronomy
Module Code	03 34469
Module Lead	Professor Igor Lerner
Level	Intermediate Level
Credits	10
Semester	Semester 2
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: Separate variables in partial differential equations. Solve partial differential equations using a variety of Fourier techniques. Add, multiply and find the determinant and inverse of a matrix. Use Gaussian elimination to solve simultaneous linear equations. Diagonalise a small matrix, determining both the eigenvalues and eigenvectors. Define and identify symmetric, anti-symmetric, Hermitian, anti-Hermitian, orthogonal, unitary, and normal matrices.
Assessment	34469-01 : Examination : Exam (Centrally Timetabled) - Written Unseen (80%) 34469-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions	Class Test (20%); 1.5 hours Examination (80%)
Other
Reading List