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Course announcements

Week	Date	Sections covered	Homework
8/22 - 8/26	8/24	Chapter 1: intro to diff equations
	8/26	2.1: linear equations	HW 1 (due Fri 9/2)
8/29 - 9/2	8/29	IODE lab: vector fields
	8/31	Chapter 1 + 2.1: theory of first-order linear equations (cont'd)
	9/2	2.2: separable equations	HW 2 (due Fri 9/9)
9/5 - 9/9	9/5	NO CLASS: LABOR DAY
	9/7	2.6: homogeneous equations, Bernoulli equations
	9/9	2.6: exact equations	HW 3 (due Fri 9/16)
9/12 - 9/16	9/12	2.6: Clairaut equations 2.8 + handout: Picard theorem, Implicit Function Theorem (intro)	IODE Project 1 (due Mon 9/19)
	9/14	2.8 + handout: metric spaces
	9/16	2.8 + handout: completeness, Contraction Mapping Principle	HW 4 (due Mon 9/26)
9/19 - 9/23	9/19	2.8 + handout: maximum metric on C[a,b], uniform convergence
	9/21	2.8 + handout: proofs of Picard Thm and Implicit Function Thm part I
	9/23	2.8 + handout: proofs of Picard Thm and Implicit Function Thm part II
9/26 - 9/30	9/26	2.3: modelling with first-order ODE's
	9/28	2.5: autonomous equations (population dynamics) Chapter 2: review for Exam I	HW 5 (due Fri 10/7)
	9/30	First midterm exam: will cover Chapters 1 and 2 (1.1,1.2,1.3,2.1,2.2,2.3,2.4,2.6,2.8)
10/3 - 10/7	10/3	2.5: autonomous equations (theory)
	10/5	3.1,4.1: introduction to higher order linear equations differential operators, principle of superposition
	10/7	3.1,3.2: homogeneous constant coefficient equations (second order) existence and uniqueness theorems	HW 6 (due Fri 10/14)
10/10 - 10/14	10/10	3.3,4.1: linear independence and the Wronskian
	10/12	3.4,4.2: complex roots of the characteristic equation
	10/14	3.5,4.2: repeated roots of the characteristic equation	HW 7 (due Fri 10/21)
10/17 - 10/21	10/17	3.5,4.2: reduction of order
	10/19	3.6: method of undetermined coefficients
	10/21	4.3,3.7: method of annihilators, variation of parameters	HW 8 (due Fri 10/28)
10/24 - 10/28	10/24	3.7,4.4: variation of parameters (continued)
	10/26	3.8: mechanical and electrical oscillation
	10/28	3.8: mechanical and electrical oscillations (continued)	HW 9 (due Fri 11/4)
10/31 - 11/4	10/31	3.9: forced oscillations, resonance
	11/2	Chapter 3/5: further theory of solutions to second order linear ODE's, introduction to special functions
	11/4	5.1,5.2: review of power series, power series solutions at ordinary points
11/7 - 11/11	11/7	5.2: series solutions at ordinary points (continued)	HW 10 (due Fri 11/18)
	11/9	5.3: series solutions at ordinary points (continued)
	11/11	Second midterm exam: will cover part of Chapter 2 and all of Chapters 3 and 4 (2.3,2.5,3.1-3.9,4.1-4.4)
11/14 - 11/18	11/14	5.3,5.4: series solutions at ordinary points (continued)
	11/16	5.4,5.5: series solutions at regular singular points (introduction), Euler equations
	11/18	5.5: series solutions at regular singular points	HW 11 (due Fri 12/2)
11/28 - 12/2	11/28	5.7: systems of first order equations: general theory
	11/30	7.3: systems of first order equations : general theory (continued)
	12/2	7.5: systems of equations with constant coefficients	HW 12 (due Fri 12/9)
12/5 - 12/9	12/5	7.6,7.8: complex eigenvalues, repeated eigenvalues
	12/7	9.1, 9.2: the phase plane, classification theorem for critical points of linear systems
	12/9	9.4,9.5: applications: population dynamics, nonlinear oscillators, etc.

Problems marked with an asterisk (*) are to be turned in. The rest are optional, for you to do on your own.

Homework 1 (due Fri 9/2):

1.1: 15*,16
1.3: 1*,2*,9,10*,15,17*
2.1: 13,14*,15,18*,32,33*

2.2: 1,2*,7*,9,17*,31,35*
2.4: 4,5*,13,14*,21*

Homework 3 (due Fri 9/16):

2.4: 28*
2.6: 7*,19,22*
Additional problem: consider y = xy' - (2/3)(y')^(3/2). (a) find a one-parameter family of linear solutions, (b) find a singular solution (Hint: graph the family of linear solutions from (a) and think about the idea of envelopes of solutions from class.)

IODE Project 1 (due Mon 9/19)

Homework 4 (due Mon 9/26):

2.8: 3,5*,9*,14* (In problem 5, you only need to turn in (a) and (c). In problem 9, you only need to turn in (a). You should do part (b) of these two problems on a graphing calculator.)
Additional problem: Consider the transformation T(x,y)=((1-y)/2,x/4). (a) Prove that this is a contractive transformation of the plane. (b) The Contraction Mapping Principle guarantees that T has a unique fixed point (x_infinity,y_infinity). Find it.

Homework 5 (due Fri 10/7):

2.3: 1*,2,5*,13*
2.5: 3,9*,14*,15*
Extra Credit 2.5: 25 (find the explicit solution x(t) in cases (a) and (b) also)

Homework 6 (due Fri 10/14):

3.1: 2,4,7*,10,11*,17*
3.3: 1,2,4*,7*,27*
4.1: 2,3,6*,19*

Homework 7 (due Fri 10/21):

3.2: 16*,23,25*
3.3: 17*
3.4: 7,11*
3.5: 1,4*,12*
4.2: 13,22*,23*

Homework 8 (due Fri 10/28):

3.6: 1,5*,9*,14*,17,26(a)*
4.3: 3,4*,21* (You do not need to find the undetermined coefficients in problem 21. After doing #21, please read the summary on page 226.)
3.7: 6*,10*,12

Homework 9 (due Fri 11/4):

3.8: 5*,7,11*,12,17*,28* (in problem 28(c), identify the points where the plot of (u,u') crosses the two axes, and describe the state of the system at those points)
3.9: 5,7*,9,12*,17*

Homework 10 (due Fri 11/18):

5.2: 1,2*,7*,12,21*
5.3: 1,3*,5,7*,23*,28*

Homework 11 (due Fri 12/2):

5.4: 3,4*,15*
5.5: 3*,6*,8,20*
5.6: 1,2*

Homework 12 (due Fri 12/9):

7.1: 1,2*
7.4: 4*
7.5: 3,5*,11*,19,31*
7.6: 2,3*
9.2: 5*,9