MATH:3600:0002 Introductn Ordinary Differential Equatns

Fall 2018 2:30P - 3:20P MWF 218 MLH

Instructor:  Dr. Isabel K. Darcy
Department of Mathematics and AMCS
University of Iowa
Office:25J MLH
Phone: 335- 0770
Email: isabel-darcy AT uiowa.edu

Office hours:
WF 9:45 - 10:15am, M 2:00 - 2:15pm WF 1:30 - 2:15pm in MLH 25J (my office), and by appointment.

Note: I will usually also be available after class on Wednesdays and Fridays (and some Mondays).

Wiki Site: https://wiki.uiowa.edu/display/3600/Class+List


Syllabus


Note: Old exams from MATH:3600 are available from my previous course websites:
          MATH:3600 Introductn Ordinary Differential Equatns (Spring 13)
          MATH:3600 Introductn Ordinary Differential Equatns (Spring 16)
          MATH:3600 Introductn Ordinary Differential Equatns (Fall 18)

Note: Old exams from 22M:034 are available from my previous course websites:
          22M:034:091 Engineering Math IV: Differential Equations 9:30A - 10:20A MWF 217 MLH(Fall 10)
          22M:034:081 Engineering Math IV: Differential Equations 8:30A - 9:20A MWF 105 MLH(Fall 08)
          22M:034:102 Engineering Math IV: Differential Eqns. 10:30A - 11:20A MWF 210 MLH (Spring 05)
          22M:034:102 Engineering Math IV: Differential Equations TR 10:55 - 12:10, 118 MLH (Fall 03)

TENTATIVE CLASS SCHEDULE-ALL DATES SUBJECT TO CHANGE (click on date/section for pdf file of corresponding class material):

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Monday Wednesday FridayHW/Announcements
Week 1 8/20:  1.1 8/22:  ch 1, 2.2 (ppt, pdf), WA, ch 1 and 2, 8/24: ; 1.2, 2.2
Week   2 8/27: ch1, 2.1, 2.2 8/29: 2.1 - 2.3 int by parts, partial fractions 1:1 8/31: 2.3, 2.4 HW 1
1.1: 1,2,11,14 - 20all, 28;
1.2: 1,7,8,9,14,17;
1.3: 1, 5, 6, 9
Week 3 9/3: Holiday 9/5:  2.4 9/7:  2.4ex p. 134, 5,
quiz 1, answers 		HW 2
1-1,
onto,
bijection
2.1: 1c, 2c, 8c, 18, 19
2.2: 1, 2, 13, 14, 25
2.3: 7-10
Week  5 9/17:  3.1 - 3.5 9/19:  review 3.1 - 3.4 9/21:  3.3, 3.4
quiz 2 (cumulative), answers 		HW 4 (due Wednesday 9/19)
p. 134, 135: 48-51
2.5: 8 (also draw the direction field), 12, 15, 20, 22
2.8: 1, 2, [3, 6 a & c -- Use induction to prove your formula for phi_n. Also prove convergence]
3.1: 2, 5
A.) By giving a specific counter-example, prove that the following functions are not linear functions: i) f(x) = \sqrt{x}.    ii) g(x) = 1/x
B.) Prove that the following functions in a linear function: h(x) = 4x
Week  6 9/24:  3.5 9/26:  2.3 #22, Review 9/28: Exam 1,   answers HW 5 (due Wednesday 10/3 -- next week, but on exam)
3.1: 8, 11, 14, 17, 21
3.2: 1, 2, 3, 9, 10, 13, 14, 15, 16, 21, 25
3.3: 1, 9, 12, 15, 18, 21
3.4: 3, 9, 12, 14
Week   7 10/1:   3.6 or 5.1, 5.2 10/3:  5.2 10/5:  5.3, 5.4 HW 5 (due Wednesday 10/3) See week above.
Week 8 10/8:  5.3, 5.4 10/10:  5.4, 10/12:  quiz 3 HW 6 (due Wednesday 10/10)
3.5: 1, 5, 11, 15, 21a, 23a, 24a, 26a
3.6: 1, 11, 13 [NOTE addition of 3.6]
5.1: 7, 8, 12, 13, 24, 28
5.2: 2
Note this is LONG HW assignment. You must provide complete answers including induction proofs.
a.) Find the recurrence relation for the power series solution about the given point x_0
b.) Find the first four terms in each of two solutions y_0, y_1 (unless series terminates sooner).
d.) Find the general term, a_n, and prove it. Determine the general solution y = a_0y_0 + a_1y_1 and determine the radius of convergence
c.) Show y_0 and y_1 form a fundamental set of solutions by evaluating the Wronskian at x_0
For more on series solutions see Paul's Online Math Notes (for printing select pdf chapter notes)
Week 9 10/15:  10/17: 10/19:  5.5 HW 7 (due Wednesday 10/17)
5.2: 7, 9, 12 (do all of a - d as you did for HW 6), 22 (for 22, you only need to approximate the solution with a cubic polynomial for 22b).
5.3: 8, 9 (but only for 5.2: 2, 7, 9, 12),   20
5.4: 2, 3, 4, 7, 10, 24
Week 10 10/22:  5.5 part 2 10/24:  Review, handout list 10/26:  Exam 2 over
3.5, 3.6, 5.1 - 5.5, 7.3
answers 		HW 8 (due Wednesday 10/31 -- next week, but 5.5 and 7.3: 16, 17 on exam)
7.2: 4, 23, 25
7.3: 15, 16, 17
-- Note this is LONG HW assignment.
5.5: 3, 7 (you must provide complete answers including induction proof and determine radius of convergence.)
Week 11 10/29:  7.1, 7.2, 7.3, E.V. 10/31: 7.1, 7.4 - 7.6, 9.1 11/2:   7.5, 7.4, 7.6, E.V. HW 8 (due Wednesday 10/31) See week above
Week 12 11/5:  7.6, 9.1 maple 11/7:  ch7, 9.1, 9.1, maple 11/9:   7.6, 9.1
double quiz 4 over ch 1, 7, and study questions, Answers 		HW 9 (due Wednesday 11/7)
7.1 (use matrix form): 4, 5, 6, 7, 15
7.4: 1, 5
7.5: 1, 5, 7, 24, 25, 27
7.6: 10
Week 13 11/12:  9.2, maple, WolframAlpha 11/14: 9.3, maple-nonlinear resonance , 11/16:  9.3 HW 10 (due Wednesday 11/14)
7.5: 19
7.6: 4
9.1: 20, 21
9.2: 5

applet??, applet

*****Thanksgiving Break****
Week 14 11/26: 9.3 11/28:  2.6 11/30: 2.6, 3.6
double quiz 5, answers 		HW 11 (due Wednesday 11/28)
1.) Fully state 7 theorems that you would prefer to prove on the final exam (over other theorems). You do not need to provide proofs for this HW, just state the theorems.
2.) State at least one theorem that you do not want to prove on the final exam.

HW 12 (due Wednesday 11/28)
9.2: 17, 18, 23, 26, 27
9.3: 5, 12
NOTE: Turn in HW's 11 and 12 in separate piles.

Read all HW answers for Ch 9 (see ICON). I STRONGLY recommend looking at each graph and determining stability type. Then check your answer by reading the text associated to the graph.
Week 15 12/3:  review 3.1 - 3.4, 3.5, 4.1, ch 4 , 5.6 12/5:  5.6, notes 12/7: Review HW 13 (due Wednesday 12/5)
Problem 1: State one interesting question that has not been answered regarding ch 9.
4.1: 4, 6, 7, 8, 18, 19bc
9.3: 7

Recommended problems (not HW):
2.6: 13, 14 (and 1 - 12)
2.8: 9a, 10a

Extra Credit (due Wednesday 12/5, 2 points for each problem added to your HW grade)
6.1: 15, 18
6.2: 2, 5, 11, 19, 20, 22
6.3: 5, 11, 14, 15, 19, 21, 34, 35
Final's Week 2013 final exam, partial answers

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