MATH2741: Methods of Mathematical Physics II

• One of: Calculus I (Maths Hons) (MATH1081) OR Calculus I (MATH1061)
• AND
• one of: Linear Algebra I (Maths Hons) (MATH1091) OR Linear Algebra I (MATH1071)
• AND
• one of: Dynamics I (MATH1607) OR Dynamics and Relativity I (MATH1627) OR Foundations of Physics I (PHYS1122)

• Mathematical Methods II (MATH2811)

• Theoretical Physics 2 (PHYS2631)

• To deepen understanding of differential equations and vector calculus in the context of solving concrete problems.
• To develop principles of applied mathematics and mathematical physics which are relevant to further physical applied mathematics modules.

• Systems of ODEs: phase plane analysis, linearisation.
• Action principles: Variational principles, Lagranges equations, Hamiltons equations, Poisson brackets, example of a charged particle in an electromagnetic field.
• Symmetries and conservation laws: Noethers theorem, including Hamiltonian and Poisson perspective.
• Fields and waves: Partial differential equations, action principles for continuous systems, wave equation, boundary conditions, Noethers theorem and stress-energy tensor.
• Static electromagnetic fields: Gauss law, Amperes law and integral forms, scalar and vector potential, Poisson equation, Greens functions, multipole expansion.
• Electrodynamics: Maxwells equations, Faradays law and integral form, electromagnetic waves, Maxwell Lagrangian and relativistic formulation.

Subject-specific Knowledge:

• Be able to analyse nonlinear systems of differential equations using linearization and phase plane analysis, as well as to understand important special classes of such systems such as Hamiltonian dynamical systems;
• Be able to understand and employ techniques from the Calculus of Variations, knowing both the mathematical ideas of deriving Euler-Lagrange equations as well as the physical interpretation of Lagrangians;
• Be able to use the formalisms of Lagrangian and Hamiltonian mechanics for particles and fields, as well as to understand their application in the development of Maxwells theory of electromagnetism;
• Be able to solve partial differential equations related to these field theories using a variety of methods, and to understand the physical content of their solutions.

Subject-specific Skills:

• In addition, students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Modelling.

Key Skills:

• Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
• Tutorials provide active problem-solving engagement and immediate feedback to the learning process.
• Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
• Summative assignments test achievement of learning outcomes and provide feedback to students about their mastery of the topics.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

If you have a question about Durham's modular degree programmes, please visit our FAQ webpages, Help page or our glossary of terms. If you have a question about modular programmes that is not covered by the FAQ, or a query about the on-line Undergraduate Module Handbook, please contact us.

Prospective Students: If you have a query about a specific module or degree programme, please Ask Us.

Current Students: Please contact your department.