Lecture Schedule and Supplementary Materials

Recommended Background for Week 1:

 

Dynamical Systems/ODE Theory:

1) Linear Stability analysis

2) Phase plane analysis

3) Hartman Grobman Theorem

4) Bifurcation theory: Definition of Saddle node, Transcritical, Pitchfork, and Hopf Bifurcation

5) Matrix Exponential

References:

1. Chapters 3, 5, 6 in

Strogatz, Steven H. Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. Chapman and Hall/CRC, 2024.

Functional Analysis:

1) Definition of bounded and closed operators

2) Definition of the resolvent and spectrum of an operator

3) Definition and properties of compact operators and operators with compact resolvent

4) Definition of the adjoint of an operator

5) Definition of a Fredholm operator

6) Sobolev Spaces and Sobolev embeddings.

References:

1. Appendix A in

Haragus, Mariana, and Gérard Iooss. Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems. Springer Science & Business Media, 2010.

2. Chapters 2.1 and 2.2 in

Kapitula, Todd, and Keith Promislow. Spectral and dynamical stability of nonlinear waves. Vol. 457. New York: Springer, 2013 

Matlab basics:

MATLAB has an onramp program that you can get yourself familiar with it quickly and in time for the summer school. To access MATLAB Onramp, you can visit https://matlabacademy.mathworks.com/en/details/matlab-onramp/gettingstarted

Here, you can click on the green “Take Course” button, which will ask you to sign in with your MathWorks Account. The course will typically take about 2 hours to complete.

Accepted students have also been emailed with more information on downloading matlab, tutorials, and a potential virtual seminar