# Unit information: Mathematical Physics 202 in 2020/21

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Unit name Mathematical Physics 202 PHYS23020 20 I/5 Teaching Block 1 (weeks 1 - 12) Professor. Rademacker Not open PHYS11400 and MATH11004, or extended mathematics units MATH11005, MATH11006, MATH11007, MATH12001. None School of Physics Faculty of Science

## Description

Physics is underpinned by a facility in mathematics. The unit introduces some core mathematical skills, building on the foundation from level C/4. The concepts of probability theory and basic statistics are introduced, relating them to situation encountered in physics. Vector methods and field theory are discussed in some depth, leading to partial differential equations and their solution by a number of methods including separation of the variable. Solutions of ordinary differential equations are covered and the concept of orthonormal basis function introduced and used. Fourier series and integrals are also emphasized.

Aims:

To introduce a number of key mathematical methods and their application to physical problems, including probability theory and statistical methods, vector field theory and solutions of partial and ordinary differential equations commonly encountered in a number of physics problems.

## Intended learning outcomes

• Understand elementary ideas of probability and able to apply these to discrete problems.
• Understand the concept of probability distributions and apply these to simple problems in quantum and statistical physics.
• Familiar with the operations of grad, div and curl and their use in vector calculus particularly in its applications to EM and fluid mechanics
• Understand the use of the Dirac delta function to model impulses and able to apply it in simple cases.
• Apply the method of separation of the variable to two- and three-dimensional problems in physics and understand the significance of boundary conditions in determining the solution.
• Able to calculate Fourier coefficients for simple periodic functions.
• Understand the relation between the width of a function and its Fourier transform, the convolution of functions and the use of Fourier transforms in problems of infinite extent and in diffraction theory.

## Teaching details

The unit will be taught through a combination of

• asynchronous online materials, including narrated presentations and worked examples
• synchronous group problems classes, workshops, tutorials and/or office hours
• asynchronous directed individual formative exercises and other exercises

## Assessment Details

Written timed, open-note examination (80%) Coursework (20%)