SI1141 Mathematical Methods in Physics, Course I 6.0 credits

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. Relation to numerical methods.

The subject of this course 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 methods to solve such models, and to give physical interpretations of the solutions.

Recommended prerequisites: Knowledge of mathematics and vector analysis corresponding to the courses given during the first two years.

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

• TENA - Examination, 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.

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

Examination in partial differential equations (TEN1; 6 university credits)

• 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.