# MAT 3306.01, Differential Equations, Spring 2019

### 11. Homework Expectations

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## Homework Assignments

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HW0:  Read and Study (R&S) pgs 1-21 in Paul's Notes.

Remember to dress up pretty for the seating chart pictures on Thursday!

Due: Start of class on Thursday, 1/17
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HW1:  a) Show that y = 7x^(-1/2) is a solution to the ode of Example 1, (pg 5) in our text.
b) Show that the given solution in Example 5 (pg 6) is valid.
c) Work problems 15-23 odd, 26 and 52 from Schaum's pgs 6-7.

R&S pgs 22-36 in our text (Paul's Notes)

Due: Start of class on Tuesday, 1/22
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HW2:  a) Work Paul's Examples 3 and 4 from 2.1 of our text (pgs 30-32).
Show all steps of simplifying and evaluation of integrals.

b) Work problems 24,34,50, and 52 from Chapter 6 of Schaum's.
Show all steps of simplifying and evaluation of integrals.

Due: Start of class on Thursday, 1/24
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HW3:  Work Schaum's problems 4.24, 4.32, 4.42 and 4.45. Show all work on each problem
and show the interval of validity for each problem.

R&S 2.3

Due: Start of class on Tuesday, 1/29
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We will have our first test over HW1, HW2 and HW3 on Thursday.
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HW4:  Do 2.3 examples 4,5 in Pauls (pgs 45-63) (exact odes).

Do the following problems from the Schaum's Chapter 5 on Exact ODEs:

Problems 4,5,26,27

How-To for Exact ODEs (corrected version)

Lecture notes over this material from a previous semester

My solutions to the schaum's 4.5, 4.26, and 4.27

Due: Start of class on Tuesday, 2/5
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HW5:  Do 2.4 examples 2 and 3 in Paul's (Bernoulli odes - pgs 60-66) like we did
example 1 in class today. Show all details of the solution on your paper, especially
the solution of the linear equation in v.

Do problems 6.17, 6.42, and 6.53 in Schaum's. State the Interval of Validity
for each problem, along with the solution.

R&S 2.5 in Paul's

Due: Start of class on Thursday, 2/7
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HW6:  Do example 2 in Paul's  Chapter 2 Section 5 (Substitutions - pgs 70-71) like we
did example 1 in class today. Show all details of the solution on your paper,
along with the Interval of Validity.

Do problems 4.11, 4.50 in Schaum's. Show all details of the solution on your paper,
along with the Interval of Validity. Obtain the General Explicit Solution, if possible.

R&S pgs 71-75 in Paul's.

Due: Start of class on Tuesday, 2/12
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We will have our second test over HW4, HW5 and HW6 on Thursday.
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HW7:  Do example 4 in Paul's  Chapter 2 Section 5 (pgs 73-75) like we did
example 3 in class today. Show all details of the solution on your paper,
along with the Interval of Validity.

Here is a link to Paul's coverage of Partial Fractions Decomposition
(Just in case you need it!)

R&S pgs 76-83  (2.6 and 2.7a) in Paul's.

Write a brief (no more than 1/2 of one page) summary of what you think was
important from the reading in Paul's 2.6. Have this ready to turn in!

Due: Start of class on Tuesday, 2/19
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HW8:  Complete the work you did in class on Tuesday in performing the details of the
integration. If your work from the board arrives at the correct answer with all
steps shown, then your board picture is all you need. If you missed class today,
do the details on paper and have it ready to turn in.

R&S pgs 83-89 in our text.

Due: Start of class on Thursday, 2/21
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HW9:  Do the following Schaum's Chapter 7 Problems:

Mixture Problems:  #'s 65,67,70 (look at #'s 16,17,18 for examples)
Population Problems: #'s 26,27,31,33,34 (look at #'s 1-7 for examples)

Do your nice write-up of Paul's 2.7 Ex 2.

Due: Start of class on Tuesday, 2/26
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HW10:  Do the following Schaum's Chapter 7 Problems:

Moving Objects Problems:  #'s 51,54,56,58,59,63
(look at #'s 11-15 for examples)

Due: Start of class on Thursday, 2/28
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HW11:  Finish the motion problems from HW10.
R&S Paul's chapter 3, sections 1 and 2 (pgs 111-121).

Due: Start of class on Tuesday, 3/5
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HW12:  Do Paul's 3.2 Examples 2 and 3;
Do Schaum's Chapter 9 problems 22,28,29,32; R&S Pauls 3.3 (pgs 122-126)

Due: Start of class on Tuesday, 3/19
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HW13:  Do Paul's 3.3 Example 1 carefully, on paper to turn in.
Try to graph your solution to Example 1.

Due: Start of class on Tuesday, 3/19
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HW14:  Do Schaums Chapter 9 Problems 20,21,24,31; R&S Paul's 3.4 (pgs 127-130)

Due: Start of class on Thursday, 3/21
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We will have our third test over HW9, HW10 and HW11 on Tuesday, 3/26.

There will be at least one each of mixture, population, and motion problems.

You may bring up to 4 study sheets, including your table of derivatives and integrals.
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HW15:  Do Schaums Chapter 9 Problems 23,26,30;
Do Pauls 3.4, Ex3; R&S Paul's 3.4 (pgs 127-130)

Summary of techniques for SOLHODEWCCs

Due: Start of class on Thursday, 3/28
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HW16: R&S Paul's 3.5, 3.6, and 3.7 (pgs 131-145)

Quick review of Cramer's Rule and the Wronskian

Find the Wronskian for the following pairs of functions:

Problem 1:  y1(x) = e2x , y2(x) = e3x

Problem 2:  y1(x) = x , y2(x) = x2 over the domain x > 0

Problem 3:  y1(x) = x2 , y2(x) = ( x )-2 over the domain x > 0

Due: Start of class on Tuesday, 4/2
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HW17: R&S Paul's 3.8-3.9 (pgs 146-164)

Due: Start of class on Thursday, 4/4
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HW18: Do Paul's 3.9 Ex 3, Ex 4 (pgs 151-152);

Do Schaum's Chapter 11, #'s 44,45,46,47;

Due: Start of class on Tuesday, 4/9
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HW19: Do Paul's 3.9 Ex 10. R&S 3.10 (pgs 165-171)

Due: Start of class, Thursday, 4/11
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HW20:  Do Paul's 3.10 Ex 2. Show ALL steps necessary to find the general solution.
Do Schaum's 11.46 (you can check your general solution in the answer's section).
In addition for Schaum's 11.46, make it an IVC problem with the following IVCs:
y(0) = 2 , y'(0) = 1 and find the Specific Solution.
Show ALL steps necessary to find the c1 and c2 and state
the specific solution.

For these two problems, write them up nicely. They will count as one page
of your final exam. They are due at the BEGINNING of class on Tuesday
and will NOT be accepted after that!

Due: Start of class on Tuesday, 4/16
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HW21:  Do Schaums 12.9, 12.13, 12.20;

Do 12.9 with the IVCs y(1) = (97/12)*e , y'(1) = (77/6)*e and find the
specific solution.

I will pick these up for a homework grade!

Variation of Parameters Method Summary

Due: Start of class, Thursday, 4/18
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HW22:  Do Schaums chapter 13 problems 4,8,11, and 12. Write them up nicely and expect
me to pick these up for a homework grade! Show all steps required for each solution.

Each solution should be the specific solution to the ODE.

(If problem 4 gives you trouble, look at problem 10.1 in Schaums as suggested).

R&S Paul's 3.11 (pgs 172-190).

Due: Start of class on Tuesday, 4/23
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HW23:  Do Pauls Ex 1 from 3.11, but change the initial conditions to an initial
displacement of down 2 feet and tossed up at 10 ft/sec. Show all work leading

R&S 3.11;

Due: Start of class, Thursday, 4/25
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HW24:  Do the following problems from Schaum's, chapter 14. Notice that Schaum's identifies
the damping force as air resistance.

14.5, 14.38, 14.41

Write these up nicely with all work shown. These will count as another page

Due: Start of class on Tuesday, 4/30
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HW25:  Last take-home questions over 3.11 for the final exam:

Problem 1:

A 3kg object is attached to a spring and will stretch the spring 392 mm by itself. There
is no damping in the system and a forcing function of the form F(t) = 10 cos(4t) is
attached to the object. If the object is initially displaced 20 cm downward from its
equilibrium position and given a velocity of 10 cm/sec upward, find the
displacement, u(t), at any time t.

Problem 2 (similar to Ex 6):

A 3kg object is attached to a spring and will stretch the spring 392 mm by itself. A
damper will exert a force of 60 Newtons when the velocity is 2 m/sec. A forcing
function of the form F(t) = 10 cos(4t) is attached to the object. If the object is
initially displaced 20 cm downward from its equilibrium position and given a
velocity of 10 cm/sec upward, find the displacement, u(t), at any time t.

Do each of the problems above.
Write them up nicely showing all work required to get the problem, including
the details of finding c1 and c2. Finish each problem by graphing your solution.
SHOW ALL WORK!

Due: By (or before) noon, Thursday, 5/9

Just slide it under my door or give it to the receptionist.
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The final exam for MAT3306.01 (the T/Th 2:40 section) is on
Thursday (May 9th) from 7:45 - 9:45AM in this room.
Bring your calculator (NOT a phone, ipad, android, or other internet capable device)

Note: On all emails for this course, start the subject line out with
MAT3306, followed by whatever else is appropriate. Emails without this
subject line formatting may not be accepted!

Last updated on ... 12/14/2018
Created on ... 12/14/2018

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