# Math 333: Differential Equations (Instructor: Sergei Chmutov)

## Spring 2000 Daily Schedule

# Date Topics Homework
0 01/30 (Tu) Introduction. Equations and their solutions. Differential equations. ODE and PDE and their solutions. Order of a differential equation. Reading: Ch. 1
1 02/01 (Th) Separable ODEs. Homogeneous Equations. Reading: Sec. 7
Assignment #1: p.49: 1(a,b,g,i), 3(a)
Due Th. Feb. 8
02/06 (Tu) Snow morning
2 02/08 (Th) Exact equations. Reading: Sec. 8
Assignment #2: p.53-54: 1, 3, 9, 17, 22(a)
Due Th. Feb. 15
3 02/13 (Tu) Linear equations. Reduction of order. Reading: Sec. 10, 11
Assignment #3: p.62: 2(a,f,g,h), p.65: 1(g)
Due Tu. Feb. 20
4 02/15 (Th) Second order ODEs. General solution. Use of a known solution to find another. Reading: Sec. 14, 15
Assignment #4: p.91: 3, 4, 6(a,b,c)
Due Th. Feb. 22
5 02/20 (Tu) Use of a known solution to find another. Homogeneous equations with constant coefficients. Reading: Sec. 16, 17
Assignment #5: p.94: 3, 4, 9,
p.97: 1(a), 2(b)
Due Tu. Feb. 27
6 02/22 (Th) The method of undetermined coefficients. Homogeneous equations with constant coefficients. Reading: Sec. 17,18
Assignment #6: p.97: 1(e,j,r)
p.103: 1(b,c,d)
Due Th. Mar. 1
02/23 (Fr) QUIZ #1 (First order ODE's. Chapter 2)
7 02/27 (Tu) The method of variation of parameters. Reading: Sec. 19
Assignment #7: p.106: 2, 3(c), 4(a,d), 6(c)
Due Tu. Mar. 6
8 03/01 (Th) Applications: Mechanics; Vibrations. Reading: Sec. 20
Assignment #8: p.113: 3,4,5,6
Due Th. Mar. 8 CANCELLED
03/06 (Tu) Snow day
03/08 (Th) Solving HW #8.
03/09 (Fr) Review for TEST #1 (Second order ODE's. Chapter 3)
03/13 (Tu) TEST #1
9 03/29 (Th) Systems of first order ODEs. Reading: Sec. 54, 55
Assignment #9: p.426: 5(a,c), 6(a,c), 7(a), 8, 9(a)
Due Th. Apr. 5
10 04/03 (Tu) Homogeneous linear systems with constant coefficients. Reading: Sec. 56
Assignment #10: p.433: 1(a,b,c,d,f)
Due Tu. Apr. 10
11 04/05 (Th) Applications: Mathematical Modeling. Population models. Logistic model. Logistic model with harvesting. No homework.
12 04/10 (Tu) Prey--predator model. Lotka--Volterra system. Reading: Sec. 57
Assignment #11
Due Tu. Apr. 17
13 04/12 (Th) Nonlinear equations and systems. Phase portrait. Reading: Sec. 58
Assignment #12: p.446: 4(b,c,d) draw the phase portraits, 6(b), 7
Due Th. Apr. 19
14 04/17 (Tu) Types of critical points. Nodes. Saddle points. Centers. Spirals (Foci). Reading: Sec. 59
Assignment #13: p.454: 1(b,c,d), 2(a,c)
Due Tu. Apr. 24
15 04/19 (Th) Critical points for linear systems. Reading: Sec. 60
Assignment #14: p.464: 1(a,c,d,f,g)
Due Th. Apr. 26
04/26 (Th) TEST #2