Mathematics for postgraduate students

O.M. Kiselev,

Innopolis University,

autumn 2021

• Introduction into mathematical modelling
• Population dynamics
• Lyapunov’s stability, limit cycles and discrete control
• Normal forms and bifurcation theory
• Elements of bifurcation theory
• Laplace transform
• Chaotic behaviour of dynamical systems
• Random walk
• Langevin and Fokker-Planck equations
• Distributions and Schroedinger equation
• Integral principles and variational calculus
• Non-convergent and asymptotic series
• Klein's model of Lobachevskii geometry
• Klein's model of Lobachevskii geometry and pseudosphere