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Fourier series and Fourier transforms are introduced as a means of representing and analysing functions of physical significance. The mathematical principles of Fourier theory are developed within the physical context of Fourier optics, diffraction theory, quantum mechanics and signal processing.
The formulation of Classical Newtonian and Lagrangian mechanics is then discussed in the context of the symmetries of nature, conservation laws, Hamilton's equations and integration of the equations of motion. These principles are applied to the description of physical and mechanical systems and includes a detailed discussion of rotational and oscillatory motion, mechanical stability, collisions, scattering, diffusion and continuum mechanics.
The emphasis in this subject will be to the development of techniques for solving problems involving a wide range of physical systems, including the formulation of appropriate mathematical and computational models and the identification of approximate solutions and limiting cases. Particular emphasis will be placed on the development of techniques that have wide applicability. Illustrative examples of these underlying principles will be drawn from classical and quantum mechanics, electromagnetism and optics, electronics, geophysics, astrophysics, physical chemistry and physical biosciences.
Intended learning outcomes
To challenge students to expand their knowledge of fundamental physics principles and develop their capacity to:
- explain diffraction physics and solve and analyse simple problems using Fourier transforms and related analytical tools.
- investigate simple problems in physical systems using the principles of classical Lagrangian and Hamiltonian mechanics, quantum mechanics or electromagnetism and appropriate methods of mathematical analysis.
A student who completes this subject should be able to:
- Explain their understanding of physics principles and applications lucidly, both in writing and orally;
- Describe the experimental and observational basis of the physical principles presented in the subject, both in writing and orally;
- Participate as an effective member of a group in tutorial discussions and study groups;
- Think independently and analytically and direct his or her own learning;
- Manage time effectively in order to be prepared for regular tutorial classes, tests, the examination and to complete assignments.
Last updated: 9 September 2021