SI1143 Mathematical Physics 10.5 credits

Vector analysis (Part 1):

Gradient, divergens and curl. The theorems of Gauss and Stokes. The nabla-operator. Simplification of vector expressions using nabla calculus and/or tensor. Orthogonal coordinates, especially cylinder coordinates and spherical coordinates. Singular vector fields, especially the point source and point vortex. Laplace- and Poisson equations. Cartesian tensors with applications to electro dynamics and continuum mechanics.

Partial differential equations (Part 2):

Physical problems that can be modeled by differential equations such as the wave equation, the Laplace- and the Poisson equation. d’Alemberts method, separation of variables, Hilbert spaces, spectral theory of self-adjoint Hilbert space operators, Sturm-Liouville systems. Separation of variables in cartesian, cylindrical and spherical coordinated; special functions like Bessel functions, Legendre polynomials and spherical harmonics.

In Part 1 the students should learn to master the tools from vector and tensor analysis that are important prerequisites for other theoretical physics courses like electrodynamics or continuum
mechanics.
The subject of Part 2 are initial- and boundary value problems for linear partial differential equations which are important in electrodynamics, quantum mechanics etc. The students should learn to formulate specific physics problems through mathematical models of this kind, to master various important analytical and numerical methods to solve such models, and to give physical interpretations of the solutions of such models.

Recommended prerequisites: To master the contents of the mathematics courses that preceed each part of this course in the course plan for the technical physics program.

Part 1: P.C. Matthews, Vector Calculus, Springer (1998) together with material to be made available on the course webpage.

Part 2: G. Sparr and A. Sparr, Kontinuerliga system, Studentlitteratur, Lund (2000) together with the "Övningsbok".

If the course is discontinued, students may request to be examined during the following two academic years.

• TEN1 - Vector Analysis, 4.5 credits, grading scale: A, B, C, D, E, FX, F
• TEN2 - Partial Differential Equations, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Edwin Langmann

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.