Mathematical Physics I

Enrollment in class

Analysis of functions of a single and several variables: Differential calculus, series, integrals, extrema, asymptotic methods, the method of stationary phase.
Vector calculus: Scalar and vector fields. Transformations of coordinate systems, rotation group and its properties. Pseudo-vectors. Differential operations over vector fields. Transport laws and continuity equations. Maxwell equations. Laplace operator. Scalar potential. Field equations: Poission equation, diffusion equation, and wave equation.
Tensor calculus: Eigenvalues and eigenvectors, diagonalization. Diadic product. Symmetric and antisymmetric tensors. Tensor fields. Stress and strain tensors. Hooke’s law. Navier-Stokes equation.
Differential equations: Systems of ordinary differential equations. Vector field picture and the concept of phase space and phase flow. Stationary points. Characterization and classification of stability of stationary points. Newton's law. Linearization. Physical pendulum and coupled oscillators. Coupled rate equations.

Kuščer, Kodre, Matematika v fiziki in tehniki.
Mathews, Walker, Mathematical methods of Physics.
Morse, Feshbach, Methods of Theoretical physics.

The course introduces applications of a number of mathematical concepts – numbers, functions, vectors, tensors, etc., in physics. It emphasises the conceptional and operational differences between practice in mathematics and physics.

Knowledge and understanding:
Understanding of general structure of the laws of physics and their underlying mathematical structures. The ability to devise precise mathematical formulations of physics problems.

Application:
Introduction to mathematical tools for the courses of theoretical physics. Gaining skills of quantitative estimation.

Reflection:
Understanding of the relation between the physical phenomena and their mathematical idealization.

Transferable skills:
Solution of a concrete project with the subject of mathematical physics and the preparation of the report.

Lectures, exercises, consultations.
Individual project.

6 written tests during semester, or written exams, required 50% score
Individual project.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

1. T. Gorin, T. Prosen, T. H. Seligman in M. Žnidarič, Physics Reports 435,
   33-156 (2006)
2. T. Prosen, Physical Review Letters 106, 217206 (2011)
3. E. Ilievski in T. Prosen, Communications in Mathematical Physics 318,
   809-830 (2013)