Introduction

In this module you will apply the mathematical language of differential equations and vector calculus to study understand phenomena in wave thoery, classical electromagnetism and fluid dynamics. We will follow three units in turn through the module:

1. Waves

   1. An introduction to oscillations and waves

   2. Derivation of the wave equation

   3. Solving the wave equation, d’Alembert wave solution

   4. Dispersion relations and wabe speed

   5. Wave energy and power

   6. Standing waves

   7. Matter waves and the Schrödinger equation

   8. Doppler shift

2. Electromagnetism

   1. Introduction electrostatics, Coulomb’s law and Gauss’s law

   2. Beginnings of magnetism up to Ampère’s law

   3. Electromagnetic induction and Faraday’s law

   4. Deriving Maxwell’s equations and electromagnetic waves

3. Fluid Dynamics

   1. Introduction to fluid mechanics

   2. Conservation of mass, energy and momentum

   3. Euler solutions and Benulli’s equation

   4. Concepts of vorticity and rotational/irrotational flow

   5. Deduce special forms of the NS equations, such as for incompressible, adiabatic flow, steady flow

   6. Investigate classic fluid phenomena, such as surface waves in deep/shallow water

Textbooks:

See the most up to date reading list on the ReadingLists@UCL page