Week	Topics	Sections	Assignment	Due date
4-Sept	Fixed points, stability, linear stability analysis	2.2,2.4	2.1.4, 2.2.1, 2.2.6, 2.2.8, 2.2.9, 2.2.12, 2.4.2, 2.4.9 (optional) [Note: We will discuss 2.2.12 - the nonlinear resistor - in class on Friday] Solutions .	12-Sept
5-Sept	Linear stability, Euler's method	2.4,2.8	Hand in the group project one or two . For the logistic population growth model with r=0.04, K=1000 and initial value N(0)=500, estimate (using Euler's method with monthly time increments) how large the population will be in one year. Compare with the real result from the project. Solutions: Group 1 Group 2(pdf files)	12-Sept
12-Sept	Bifurcations	3.1,3.1,3.4	3.1.1,3.1,3.,3.2.3,3.2.4,3.4.4,3.4.6,(optional 3.4.14) Solutions	17-Sept
17-Sept	Bifurcations. One-dimensional maps.	3.6,10.1	3.6.3, 10.1.9,10.1.11 Solutions	26-Sept
26-Sept	Lyapunov exponent	3.1,3.1,3.4	10.3.5, 10.3.10, 10.5.1, 10.5.2, 10.5.7 Solutions	10-Oct
17-Oct	Linear systems. Classification	5.1,5.2,5.3	Option 1: 5.1.9, 5.1.10 (a)&(e), 5.2.8, 5.2.13 Option 2: 5.2.11, 5.3.3, 5.3.4, 5.3.5, 5.3.6 Solutions Option 1 and Option 2	26-Oct
29-Oct	Phase portraits. Conservative systems	6.1,6.3,6.5	6.3.10, 6.3.14, 6.5.1, 6.5.2 Solutions	7-Nov
14-Nov	Limit cycles. Gradient systems, Lyapunov functions	7.1,7.2,7.3	7.2.9(a & c), 7.2.12 Solutions	26-Nov
5-Dec	The Lorenz system. Cantor sets. Fractal and box dimension.	9.2,11.2,11.3,11.4	9.2.1,11.2.5,11.3.2,11.3.4, 11.3.7,11.3.9,11.4.1,11.4.2	14-Dec