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:
MWF 9:45 - 10:10am, WF 1:30 - 2:15pm, W 3:30 - 3:45++ in MLH 25J (my office), and by appointment.
Note: ++ means I will be also available directly after the office hour, normally for as long as needed.
I will usually also be available after class on 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)

Integration Pre-requisites:

The following online book contains many nice examples and good explanations: Paul's Online Notes: Differential Equations

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

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, int by parts
Week   2 8/27: partial fractions, ch1, 2.1, 2.2 8/29: 2.1 - 2.3 1:1 8/31: 2.3, 2.4, (WA), maple (pdf) HW 1 (due Wednesday 8/29)
1.1: 1,2,10 - 16 all, 21, 23;
1.2: 1,5,7,8, 13;
1.3: 1, 2, 6, 9, 12
Week 3 9/3: Holiday 9/5:  2.4 9/7:  2.4ex p. 134, 5,
quiz 1, answers 		HW 2 (due Wednesday 9/5)
1-1,
onto,
bijection
2.1: 1c, 2c, 11, 12, 19
2.2: 1, 2, 11, 13, 25
2.3: 5-7
Week 4 9/10:  Ex 2.4, 2.5 ex, IVP ex, Ex 2.4.1, 9/12: 2.5, 2.8 9/14:  2.8, linear fns, HW 3 (due Wednesday 9/12)
2.3: 12, (16-19)a
2.4: 1, 4, 5, 6, 11, 12, 17 - 21, 23 - 25, read 26
p. 101: 28, 32, 35
Week  5 9/17:  3.1 - 3.5, ratio test 9/19:  review 3.1 - 3.4 9/21:  3.3, 3.4
quiz 2 (cumulative), answers 		HW 4 (due Wednesday 9/19)
p. 101: 36, 37
2.5: 2, 4, 7, 9 (also draw the direction field for 7 and 9), 15, 19, 21
2.8: 1, 2, [3, 4 a & c -- Use induction to prove your formula for phi_n. Also prove convergence]
Week  6 9/24:  2.3 #22, Review 9/26: Exam 1,   answers 9/28:  3.2, 3.5 HW 5 (due Wednesday 9/26)
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
3.1: 2, 4, 6, 10, 12, 13, 21
3.3: 1, 6, 9, 12, 13
3.4: 3, 10, 11
Week   7 10/1:   3.5, answers, example 10/3:  5.1, 5.2 10/5:  5.2 HW 6 (due Wednesday 10/3)
3.2: 1, 2, 3, 7, 8, 10 - 13, 16, 20
Week 8 10/8:  5.3, 5.4 10/10:  5.4, 10/12:  quiz 3 answers HW 7 (due Wednesday 10/10)
3.5: 1, 4, 8, 9, 11, 16a, 17a, 18a, 19a
5.1: 3, 6, 10, 11, 20, 23
5.2: 3
Note this is LONG HW problem. 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).
c.) 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
d.) 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: 5.5 10/19:  5.5 part 2, 7.3, E.V. HW 8 (due Wednesday 10/17)
5.2: 7, 9, 14 (for 7, 9, 14, do all of a - d as you did for HW 7), 19 (for 19, you only need to approximate the solution with a cubic polynomial for 19b).
5.3: 6, 7 (but only for 5.2: 3, 7, 9, 14),   16
5.4: 2, 3, 4, 5, 8, 15, 23
Week 10 10/22:  5.5, study question, Answers 10/24:  Review, handout list 10/26:  Exam 2 over
3.5, 5.1 - 5.5, 7.3
answers 		HW 9 (due Wednesday 10/31 -- next week, but 5.5 and 7.3: 14, 15 on exam)
7.1 (use matrix form): 3, 4, 5, 6, 12
7.2: 4, 17, 19
7.3: 13, 14, 15
-- Note this is LONG HW assignment.
5.5: 3, 6 (you must provide complete answers including induction proof and determine radius of convergence.)
Week 11 10/29:  7.1, 7.4 10/31: 7.4 - 7.6, 9.1 11/2:   7.5, 7.4, 7.6, E.V. HW 9 (due Wednesday 10/31) See week above
Week 12 11/5:  7.6, 9.1 maple 11/7:  7.6, WA 11/9:   ch 9
double quiz 4 over 2.1 and 7.5, answers 		HW 10 (due Wednesday 11/7)
7.4: 1, 7, 11
7.5: 1, 2, 5, 17, 18, 19
7.6: 8
Week 13 11/12:  graphs, ch 9, 9.3, WolframAlpha 11/14:  ch 9 11/16: 9.3 HW 11 (due Wednesday 11/14)
7.5: 13, 21
7.6: 4
9.1: 17, 18
*****Thanksgiving Break****
Week 14 11/26:  ch 9, maple, maple, maple-nonlinear resonance , 11/28: 3.6, Review 2.8, ch 5, slope fields 11/30: 3.6
double quiz 5: 2.8, ch 5, 2.5, ch 9, answers
  • Be able to estimate the solution to a differential equation using 2.8 or ch 5 methods.
  • Be able to draw direction fields, trajectories (including when given initial values), and determine stability for both first order (2.5) and systems of first order (ch 9) for autonomous differential equations. See practice quiz, COMPLETE answers
HW 12 (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 13 (due Wednesday 11/28)
9.1: 15, 17, 18
9.2: 22, 23
9.3: 4 (use computer for part d)
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. Note answers are from an older edition so not all problems match your HW (and many are numbered differently)

You should check your answers, but all answers must be in your own words.

Week 15 12/3:  review 3.1 - 3.4, 3.5, 4.1, ch 4 12/5: Review: Induction (2.8, ch 5) 12/7: Review HW 14 (due Wednesday 12/5)
Problem 1: State one interesting question that has not been answered regarding ch 9.
3.6: 9, 10
4.1: 1, 4, 5, 7, 13, 14bc
4.3: 7
4.4: 2 (solve using both method of undetermined coefficients and variation of parameters).
9.1: 17, 18
9.2: 4, 14, 15, 19 (use computer for part b)
9.3: 6, 9 (use computer for part d)

Final's Week Final exam: 12/12/2018 8:00PM - 10:00PM 218 MLH 2013 final exam, partial answers
2016 final exam, partial answers
7.7




5.6, notes

9.3 df applet??, applet