Mathematical Physics modules

For a full description, click on the module number or scroll down the page:

MP350 - Classical Mechanics
MP352 - Special Relativity
MP353 - Fluid Mechanics
MP354 - Computational Physics 1
MP361 - Ordinary Differential Equations
MP363 - Quantum Mechanics

Classical Mechanics - MP350

Semester 1, 5 credits, 24 lecture hours, 8 tutorial hours

Module objectives

To give the students a solid understanding of classical mechanics in the Lagrange-Hamilton formalism. On completing the module, the students shall be able to

formulate the basic principles of the Lagrange-Hamilton formalism, and use them to derive equations of motion for dynamical systems
explain the relation between symmetries and conservation laws, and apply conservation laws to analyse the motion of dynamical systems
describe the mathematical properties of rotations and systems with rotational symmetry

Module content

Lagrange theory: Hamilton's Principle of least action, Euler-Lagrange equations, canonical momenta and conservation laws. Central forces. Two-body motion: bound states. Rigid Body Motion: Rotation transformations, Euler's theorem, inertia tensor, Euler's equation of motion, the heavy symmetrical top, small oscillations and stability. Hamiltonian theory: The canonical equations, Poisson brackets.

Assessment

Total Marks 100%. 1½ hour written examination at the end of Semester 1 80%. Continuous assessment 20%.

Link to course pages

Special Relativity - MP352

Semester 2, 5 credits, 24 lecture hours, 8 tutorial hours

Module objectives

To understand the physics of Special Relativity. To apply relativity to physical problems and calculate relativistically invariant quantities.

On successful completion of the module, students should be able to:

explain the need for Einstein's two postulates
perform calculations using four-vectors in Minkowski space
calculate time dilation, length contraction effects and explain the twin paradox
formulate relativistic kinematics and carry out standard computations
appreciate the experimental validity of special and general relativity

Module content

The ether, Michelson-Morley experiment, Lorentz transformations, Minkowski space, length contraction and time dilation, relativistic kinematics, four vectors, relativistic optics and electromagnetism, experimental tests of relativity, GPS, Einstein's 1905 papers.

Assessment

Total Marks 100%. 1½ hour written examination at the end of Semester 2 80%. Continuous assessment 20%.

Link to course pages

Fluid Mechanics - MP353

Semester 2, 5 credits, 24 lecture hours, 8 tutorial hours

Module objectives

The aim of this course is to introduce students to the key concepts and applications of Fluid Mechanics. On successful completion of the module, students should be able to:

enumerate the basic variables and forces involved in the description of stationary and moving fluids
derive the equation of conservation of mass and deduce basic consequences from it
use Bernoulli's principle to relate velocity and pressure in a fluid
employ the concepts of vorticity, viscosity and Reynolds number in the description of fluid motion
use the Euler and Navier-Stokes equations to analyse fluid flow and drag forces in simple geometries (flow through straight pipes, between flat plates etc.)

Module content

Kinematics of fluid motion. Euler's equations, steady flow. Bernoulli's equation. Circulation. Kelvin's theorem. Velocity potential for two and three dimensional flows. Sources, sinks and doublets. The complex potential. Method of images. Vortex lines. Supersonic flow. Viscosity. Viscous flow. Navier Stokes' equation. Reynold's number. Turbulence. Poiseuille flow. Couette flow. Kolmogorov Scaling.

Assessment

Total Marks 100%. 1½ hour written examination at the end of Semester 2 80%. Continuous assessment 20%.

Link to course pages

Computational Physics 1 - MP354

Semester 2, 5 credits, 12 lecture hours, 24 laboratory hours

Module objectives

To acquaint students with use of computers for solving physical problems. On completing the module, the students shall be able to

recognise and use basic programming structures (variables, expressions, functions, control statements);
analyse the truncation error of numerical differentiation and integration schemes;
perform numerical integration of ordinary differential equations;
apply these skills to solving physical problems;
present project results in a coherent report.

Module content

Each Lecture is followed by 2 hours laboratory work. Introduction to Unix. Intoduction to MATLAB. Error, accuracy and stability. Integration. Root finding. Newton-Raphson. Ordinary Differential Equations: Euler method. Runge-Kutta method.

Assessment

Total Marks 100%. Continuous assessment 20%; 1½ hour written examination at the end of Semester 2 40%; Project 40%.

Link to course pages

Ordinary Differential Equations - MP361

Semester 1, 5 credits, 24 lecture hours, 8 tutorial hours

Module objectives

To study the principal kinds of linear ordinary differential equations. On successful completion of the module, students should be able to:

recognise the category to which an ordinary differential equation belongs
solve differential equations with constant and variable coefficients
construct Greens' functions
solve differential equations by expansion in power series
construct, and estimate convergence of, Fourier series

Module content

Linear differential equations, ordinary differential equations, complete analysis of equations with constant coefficients, equations with variable coefficients, initial and boundary value problems, Green's functions, solution by expansion in power series, treatment of regular singular points, Fourier series, Gibbs' phenomenon for Fourier series.

Assessment

Total Marks 100%. 1½ hour written examination at the end of Semester 1 80%. Continuous assessment 20%.

Link to course pages

Quantum Mechanics - MP363

Semester 1, 5 credits, 24 lecture hours, 8 tutorial hours

Module objectives

To understand the physics of quantum mechanics. On successful completion of the module, students should be able to:

explain the Planck radiation law and the significance of the photoelectric effect
pass between differential equation and operator formulations of quantum mechanics
work with quantum mechanical Hilbert space formalism
obtain the energy levels and eigenstates for the harmonic oscillator
calculate quantum tunneling amplitudes

Module content

The ultraviolet catastrophe, Planck's solution to the ultraviolet catastrophe, Photoelectric effect, Heisenberg's uncertainty principle, Observables,Schrödinger wave equation, Probabilistic interpretation of the wave function, Hilbert space formalism, Simple piecewise linear potentials, Tunnelling, Harmonic oscillator, Ladder operators, Angular momentum algebra, Bell's inequalities.

Assessment

Total Marks 100%. 1½ hour written examination at the end of Semester 1 80%. Continuous assessment 20%.