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).

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 16)

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):

Tentative exam dates: 9/26 and 10/26

9.3 df 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

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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