22M:100:001 (MATH:3600:0001) Introductn Ordinary Differential Equatns

### Should you buy the 8th or 9th edition of Boyce and DiPrima

Instructor:  Dr. Isabel Darcy

Office: B1H MLH               Phone: 319-335-0778         Email: idarcymath+100 AT gmail.com or isabel-darcy AT uiowa.edu

# Finals Week Office Hours: Tuesday 11am - 12:30, Thursday Problem Session at 3pm - 5pm in 205 MLH and Thursday 10:40 - 12:15pm, Friday 10am - 12noon and 1pm - 2:30 pm and by appt.

## Final Exam Fri 5/17/2013 3:00 PM - 5:00 PM, NOTE: LOCATION 205 MLH You may bring a 3x5 card to the exam, but no calculator. Newly posted handouts: Exam 2, answers , 9.3

Syllabus

Linear Algebra

HW 1 (due 2/6)
1-1,
onto,
bijection
1.1: 1,2,11,14 - 20all, 28;
1.2: 1,7,8,9,14,17;
1.3: 1, 3, 5, 9
2.1: 1c, 2c, 8c, 18, 19
2.2: 1, 2, 13, 14, 25

HW 2 (due 2/13) -- note same day as first quiz
2.3: 7-10, 16, (20-23)a, 25a, 29
2.4: 1, 2, 8, 9, 15, 16, 21 - 25, 27 - 31, read 32
p. 134, 135: 36, 42, 47 (note p. 134,5 in 9th edition = p. 133 in 8th)
AND

HW 3 (due 2/20)
p. 134, 135: 48-51 (note p. 134,5 in 9th edition = p. 133 in 8th)
2.5: 8 (also draw the direction field), 12, 15, 20, 22
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

HW 4 (due 2/27) (if you are using the 8th edition, see conversion )
3.1: 8, 11, 14, 17, 21
3.2: 1, 2, 3, 9, 10, 13, 14, 15
3.3: 1, 9, 12, 15, 18, 21
3.4: 3, 9, 12, 14

HW 5 (due 3/6) (if you are using the 8th edition, see 3.5 conversion )
3.5: 1, 3, 9, 13, 19a, 21a, 22a
5.1: 7, 8, 12, 13, 24, 28

HW 6 (due 3/13)
5.2: 2, 7, 9, 12, 22
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
Note that a - d applies only to the first 4 problems. For 22, you only need to approximate the solution with a cubic polynomial for 22b.
For more on series solutions see Paul's Online Math Notes (for printing select pdf chapter notes)

HW 7 (due 3/27) [except for 5.3:20, this is a short HW assignment, so get an early start on long HW 8]
5.3: 8, 9 (but only for 5.2: 2, 7, 9, 12),   20
5.4: 2, 3, 4, 7, 10, 24

HW 8 (due 4/3) [long assignment]
7.2: 4, 23, 25
7.3: 15, 16, 17
4.1: 4, 6, 7, 8, 18, 19bc
5.5: 3

HW 9 (due 4/10)
7.5: 1a, 5a, 7a, 19, 24, 25, 27
7.1 (use matrix form): 4, 5, 6, 7, 15

HW 10 (due 4/17)
5.5: 7 (you must provide complete answers including induction proof and determine radius of convergence.)
7.4: 1, 5
7.6: 4, 10

HW 6 redo due 4/11 by noon

HW 11 (due 4/24 at the beginning of class)
9.1: 20, 21
9.2: 5
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.

HW 12 (due 5/1)
Problem 1: State one interesting question that has not been answered regarding ch 9.
9.2: 17, 18, 23, 26, 27
9.3: 5, 12

HW 13 (due 5/8)
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.

Recommended problems (not HW):
2.6: 13, 14 (and 1 - 12)
2.8: 1, 2, [3 - 6 a & c], 9a, 10a

6.1: 15, 18
6.2: 2, 5, 11, 19, 20, 22
6.3: 5, 11, 14, 15, 19, 21, 34, 35

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

 Monday Wednesday Friday Week 1 1/23:  1.1 1/25:  ch 1, 2.2 , Ex 2.4.1 Week 2 1/28:  1.2, 2.2 ex 1/30: ch1, 2.1, 2.2 , df 2/1: 2.1 - 2.3 int by parts Week 3 2/4: 2.3, 2.4 2/6:  2.4 2/8:  2.4ex partial fractions p. 134, 5 (133 in 8th ed) Week 4 2/11:  ex, IVP ex, Ex 2.4.1, 2/13: 2.5, quiz 1, answers, 2/15:  2.5, linear fns, 3.1 Week 5 2/18:  3.2, 3.3, 3.4 2/20: review 3.1 - 3.4 2/22:  3.2, 3.3, Week 6 2/25:  2.3 #22, 3.2, Review 2/27:  Exam 1,   answers 3/1:  5.1, 3.2, 3.5 Week 7 3/4:   3.5, 5.1 3/6:  5.1, 5.2 3/8:  5.2 Week 8 3/11: 5.2 3/13: 5.3, 5.4 3/15: 5.3, 5.4 Spring break 3/18 - 3/22 Week 9 3/25:  5.4, 3/27: 4.1, 5.5 3/29:  5.5 part 2 Week 10 4/1:  7.1, 7.2, 7.3, E.V. 4/3:  7.5, 7.4, Quiz 2 over 7.2, 7.3 Answers 4/5: 7.5, 7.4 Week 11 4/8:  7.6 E.V. 4/10: 7.6, 9.1 maple 4/12:  ch7, 9.1, 9.1, maple Week 12 4/15:  9.2 4/17:  9.2, Quiz 3: Ch 5, Ch 7, Answers 4/19: 9.3 resonance , Week 13 4/22: 9.3 4/24:  Review 4/26:  Exam 2 answers in 301 VAN Week 14 4/29:  9.3 5/1:  2.6 5/3: 2.6, 2.8 Week 15 5/6:  2.8, review 3.1 - 3.4, 3.5, ch 4 5/8: 3.6, 5.6 5/10: Revew

Final Exam Fri 5/17/2013 3:00 PM - 5:00 PM, NOTE: LOCATION 205 MLH

Newly posted handouts: Final exam