Column Date below is filled with dates for sections I (Prof. Lushnikov) finished lecturing on. LP means Lawrence Perko's book. Homeworks ares due on Tuesdays (I pick up homework before lecture start) for all sections assigned from the previous week. For your convenience I also include due date for each homework assignment in column Due date. Currently there are topics listed for all the material I plan to cover. However, I might decide to change some of them as the semester progresses, perhaps even adding or deleting topics. Please return to this page periodically to make sure you are working the correct homework problems.
|
|
Date |
|
|
Due date |
|
|
|
|
Hw 1: |
|
|
1 |
|
LP Chapter 1. Solutions and IVPs; Linear systems |
|
|
|
2 |
|
LP Chapter 1. Linear Systems
with constant coefficients. matrix exponentials and fundamental solutions. |
|
09/01/26 |
|
|
|
|
|
|
|
3 |
08/25/26 |
LP Chapter 1. Linear Systems with constant coefficients; distinct and equal real roots |
LP 1.2 p.9: 1(a),2,3(c),6 LP 1.4 p.19: 4 LP 1.7 p.37: 1(a),2(b) |
09/01/26 |
|
4 |
08/27/26 |
LP Chapter 1. Linear Systems with constant coefficients: complex roots; Operators and Norms. |
LP 1.5 p.26: 1(a,b,c),5 LP 1.3 p.15: 1(a,b,c),3,7(a) |
09/01/26 |
|
|
|
|
Hw 2: |
|
|
5 |
09/01/26 |
LP Chapter 1. Linear Systems with constant coefficients: general case. Handouts for matrix exponent. |
LP 1.6 p.32: 2,4 LP 1.7 p.37: 3(d,f) |
09/15/26 |
|
6 |
09/03/26 |
LP Chapter 1. Jordan canonical form |
LP 1.8 p.47: 2(a,b,c,d),4,7,10 LP 1.3 p.15: 2, 5 |
09/15/26 |
|
|
|
|
|
|
|
7 |
09/08/26 |
LP Chapter 1. Stability Theory. Nonhomogeneous Systems |
LP 1.9 p.58: 2(b,d), 3 |
09/15/26 |
|
8 |
09/10/26 |
LP Chapter 2.Nonlinear autonomous systems-generalities LP Chapter 2. Existence-uniqueness theorem |
LP 1.10 p.62: 1,2,3(optional for extra credit) LP 2.1 p 69: 1(a,c)(see also Remark 1),2,3 LP 2.2 p. 77: 1,2 |
09/15/26 |
|
|
|
Hw 3: |
|
|
|
9 |
09/15/26 |
LP Chapter 2. Existence-uniqueness theorem |
LP 2.1 p 69: 4,5 LP 2.2 p. 77: 4,5(optional),6,9,10(optional) |
10/06/26 |
|
10 |
09/17/26 |
LP Chapter 2. Dependence on initial conditions. |
LP 2.3 p. 84: 1,2,5,6 |
10/06/26 |
|
|
|
|
|
|
|
11 |
09/22/26 |
LP Chapter 2.Intervals of existence; flows |
LP 2.4 p. 94: 1(a,b) |
10/06/26 |
|
12 |
09/24/26 |
LP Chapter 2.Intervals of existence; flows. |
LP 2.4 p. 94: 2(b),3 |
10/06/26 |
|
|
|
|
||
|
13 |
09/29/26 |
Test 1 in Class. No hw due on 09/29/26 |
|
|
|
14 |
10/01/26 |
LP Chapter 2.Intervals of existence; flows. LP Chapter 2.The variational equation. Linearization. The Stable Manifold Theorem |
LP 2.4 p.94: 5 LP 2.5 p.100: 1,3,6,7 |
10/06/26 |
|
|
|
Hw 4: |
|
|
|
15 |
10/06/26 |
LP Chapter 2.The Stable Manifold Theorem |
LP 2.6 p.104: 1,2,3 LP 2.7 p.117: 1,2,4,5,6, 7(optional) |
10/20/26 |
|
16 |
10/08/26 |
Fall break |
|
|
|
|
|
|
|
|
|
17 |
10/13/26 |
LP Chapter 2.The Stable manifold Theorem |
LP 2.9 p134: 2,4,5(b)(use stronger criterion for instability and try a quadratic function as U; analyze only origin, i.e. skip other equilibrium points), 5(d) (optional problem for extra credit; also analyze only origin, i.e. skip other equilibrium points),7,8, Problems |
10/20/26 |
|
18 |
10/15/26 |
LP Chapter 2.The Stable manifold Theorem; Stability; Lyapunov functions; Handouts: Criterion for Instability; |
10/20/26 |
|
|
|
|
Hw 5: |
|
|
|
19 |
10/20/26 |
LP Chapter 2. Critical points in R2 |
|
11/10/26 |
|
20 |
10/22/26 |
LP Chapter 2.Center Manifold Theorem; Normal Forms |
|
11/10/26 |
|
|
|
|
|
|
|
26 |
10/27/26 |
LP Chapter 2.Center Manifold Theorem; Normal Forms |
|
|
|
22 |
10/29/26 |
LP Chapter 2.Normal Forms. |
|
11/10/26 |
|
|
|
|
|
|
|
23 |
11/03/26 |
LP Chapter 2.Normal Forms. Gradient and Hamiltonian Systems |
|
11/10/26 |
|
24 |
11/05/26 |
Test 2 in Class. |
|
|
|
|
Hw 6: |
|
||
|
25 |
11/10/26 |
LP Chapter 3.Dynamical systems and Global Existence Theorems. |
|
11/24/26 |
|
26 |
11/12/26 |
LP Chapter 3. Dynamical systems and Global Existence Theorems. Limit Sets. |
|
11/24/26 |
|
|
|
Hw 7: |
|
|
|
27 |
11/17/26 |
LP Chapter 3. Stability of Periodic Orbits; The Poincare Map. |
11/24/26 |
|
|
28 |
11/19/26 |
Stability of Periodic Orbits; The Poincare Map. Floquet theory. |
|
11/24/26 |
|
|
|
Hw 8: |
|
|
|
29 |
11/24/26 |
The Stable Manifold Theorem for Periodic Orbits. 3.7 Poincare-Bendixson theory. 3.9 Bendixson`s and Dulac`s criteria |
|
12/01/26 |
|
30 |
11/26/26 |
Thanksgiving |
|
12/01/26 |
|
|
|
Hw 9: |
|
|
|
31 |
12/01/26 |
LP Chapter 3. Hill equation. Mathieu equation. Hill equation. Introduction to perturbation theory. |
12/05/26 |
|
|
32 |
12/03/26 |
The Averaging theorem for 1d systems |
|
|
|
|
|
|
|
|
|
|
TBA |
FINAL EXAM TBA |
|
|