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Semester 2 - Dual-Delivery
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This subject gives an example-oriented overview of various advanced topics that are important for mathematical physics and physics students, as well as being of interest to students of pure and applied mathematics. These topics include:
- Further differential equations: Bessel functions, Legendre polynomials, spherical harmonics and applications such as the Laplace/Schrodinger equation in polar/spherical coordinates;
- Further vector calculus: Differential forms, integration, Stokes’ theorem and applications such as Maxwell’s equations, charge conservation and Dirac monopoles;
- Hilbert spaces: L2 spaces, bounded and unbounded operators, normalisable and non-normalisable eigenfunctions, distributions and applications to quantum theory;
- Group theory: Lie groups and algebras, representations and applications such as quantum spin and particle physics.
Intended learning outcomes
On completion of this subject, students should be able to:
- Communicate the importance of advanced mathematical structures in conceptual and computational approaches to mathematical physics;
- Recognise that special functions naturally arise when solving physically important partial differential equations in curvilinear coordinates;
- Argue how the language of differential forms both simplifies and greatly enhances the scope of multivariable calculus and its applications in physics;
- Analyze topological concepts through the use of examples of physical phenomena;
- Articulate how the eigentheory of Hilbert space operators underlies the modern approach to quantum physics;
- Model symmetries of physical systems using basic examples of groups and Lie algebras.
In addition to skills that are useful in careers in science, engineering, commerce and education, students will develop useful generic skills that include:
- The problem-solving skills of identifying strategies to solve unfamiliar problems;
- The analytic skills of constructing and expressing logical arguments, and of working in abstract, general terms to clarify and improve available solutions;
- The time-management skills of meeting regular deadlines while balancing competing commitments.
Last updated: 17 May 2021