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## Syllabus for

FTF131 - Mathematical physics

Owner: TKTFY
4,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Engineering Physics
Department: 16 - PHYSICS

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0100 Examination 4,5 c Grading: TH 4,5 c 11 Jan 2016 pm M, 04 Apr 2016 pm M, 22 Aug 2016 am M

#### In programs

TKTFY ENGINEERING PHYSICS, Year 3 (elective)

#### Examiner:

Professor  Henrik Johannesson

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Course specific prerequisites

Basic courses on calculus, diffrential equations, complex analysis, and linear algebra.

#### Aim

Mathematics has proven to be inexplicably successful in describing natural phenomena, to the extent that it can be regarded as the language of physics. In this course we will refresh much of the mathematical knowledge that you have learned in other courses, apply it to various physical systems, and even
learn some new mathematical techniques that are a useful part of a physicist's
vocabulary. We will focus on analytic methods, and discuss computational
approaches only in exceptional cases.

#### Learning outcomes (after completion of the course the student should be able to)

- construct and analyze quantitative models for naturally occuring phenomena
- apply exact and approximate methods to evaluation of sums and integrals, and to solution of
differential and integral equations
- formulate physical laws in terms of variational principles and discuss the consequences of variational
principles on the behaviors of physical systems
- perform symmetry analysis of simple systems

#### Content

1. Differential equations: a review,
2. Evaluation of integrals: standard techniques, method of
3. Hilbert spaces,
4. Green's function,
5. Integral equations: separable kernels, Neumann and Fredholm series,
Schmidt-Hilbert theory,
6. Calculus of variations: functional derivatives, Euler-Lagrange equation,
7. Introduction to groups and representations.

#### Organisation

Lectures and recitations.