Lecture Notes for Computational Methods for Nonlinear Systems

Overview, introduction, and programming

• Introduction to course and modules (8/29/08)
• Introduction to Python and external packages for scientific computing (8/29/08)
• Introduction to SciPy and arrays (9/12/08)
• IPython tips
• NumPy/SciPy array tips

Lecture notes for computational modules

• Complex networks, small worlds, and percolation
• Pendulum and Walker
• Pattern formation, cardiac dynamics, and spiral waves
• The 2008 U.S. Presidential Election
• Bifurcations & Chaos in Iterated Maps I: Chaos & Lyapunov Exponents / Invariant Measure
• Biomolecular networks: Stochastic Cells and the Repressilator
• NP-completeness, computational complexity, and phase transitions
• Ising model algorithms and Markov chains
• Molecular dynamics, DigitalMaterial, and design patterns

• Random walks
• Universality in random matrices and extreme value statistics
• Universality, the renormalization group, and the onset of chaos