On multiscale methods for dynamical systems, Markov chains, and PDEs, part I

The lectures are meant to give introductions to non-experts, and we shall therefore only treat the basic concepts and ideas and omit many technical subtleties or generalizations.
Some useful references are

• Sanders, Verhulst, Murdock, Averaging methods
• Pavliotis, Stuart, Multiscale techniques

and for the background, for example

• Berglund, Gentz, Noise-induced phenomena
• dal Maso, Gamma-convergence
• Jost, Dynamical systems
• Jost, Partial differential equations
• Jost, Li-Jost, Calculus of variations

and others.