Module PHYS2611: MATHEMATICAL METHODS IN PHYSICS

Department: Physics

PHYS2611: MATHEMATICAL METHODS IN PHYSICS

Prerequisites

• Foundations of Physics 1 (PHYS1122) AND (Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR Core Mathematics A (MATH1012).

Corequisites

• None

Excluded Combination of Modules

• Analysis in Many Variables II (MATH2031).

Aims

• This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.
• It supports the Level 2 modules Foundations of Physics 2A (PHYS2611) and Foundations of Physics 2B (PHYS2621) by supplying the necessary mathematical tools.

Content

• The syllabus contains:
• Vector algebra including vector and scalar product.
• Differential vector operators, div grad and curl. • Divergence and Stokes theorems.
• Orthogonal curvilinear coordinates.
• Fourier series, orthogonality and Fourier coefficients.
• Fourier transforms, Dirac delta function.
• Systems of linear equations, matrices, determinants, eigenvalues and eigenvectors.
• Ordinary differential equations.
• Series solution for linear differential equations.
• Bessel's equation.
• Laplace transform and applications to ODEs.
• Examples of Partial differential equations in physics.
• Solution by separation of variables.
• Laplace's equation and its solution in different coordinate systems.
• Legendre polynomials and spherical harmonics.
• The heat equation, the wave equation and the uniqueness of solutions.

Learning Outcomes

• Having studied this module students will be familiar with some of the key results of vectors, vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, orthogonal functions, the use of matrices, and with important mathematical tools for solving ordinary and partial differential equations occurring in a variety of physical problems.

• In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.
• They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.

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Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Teaching will be by lectures and tutorial-style workshops.
• The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links on DUO.
• Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.
• Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.
• Student performance will be summatively assessed through an examination and problem exercises. The examination and problem exercises will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises and workshops provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Workshops and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University