Teaching

Lectures & Tutorials

Spring 2023/2024
When and where = Tuedays (9:50-12:10) in MUUK (3rd floor in Karlin)
Language: Czech or English
Requirements for exam: To pass the exam, students should prove understanding of the fundamental parts of the theory and ability to solve typical problems.
To get to the exam, students have to solve a project assignment, pass a midterm (písemka v půlce semestru), and solve the homeworks.
Assignments and study materials will be available in MS Teams.
Some content is based on our book.

Approximate syllabus (will be adapted to the students):

Principle of least action, Hamilton canonical equations. Cornerstones of differential geometry, Lie groups and algebras, duals of Lie algebras. Euler-Poincare equations, rigid body rotation. Infinite-dimensional Lie groups and fluid mechanics.
Lagrangian and Eulerian fluid mechanics, solids, viscoelastic fluids.
Principle of maximum entropy. Liouville and Boltzmann entropy. Sackur-Tetrode relation for ideal gases.
Reversibility and irreversibility. Dissipation potential. Energetic and entropic representations. Second law of thermodynamics.
General Equation for Non-equilibrium Reversible-Irreversible Coupling (GENERIC).
Liouville equation and kinetic theory. Electromagnetic fields and their interaction with matter.
Mixtures, hyperbolic evolution and Maxwell-Stefan equation, Fick's and Ohm's law. Hyperbolic heat conduction and Fourier's law.
Fluctuations, Wiener processes, fluctuation dissipation theorem, Fokker-Planck equation, Ito calculus.
Keywords: Hamiltonian dynamics, Poisson bracket, energy, entropy, dissipation potential, GENERIC, continuum mechanics, principle of maximum entropy.