Syllabus

Schedule and Homework
Syllabus

Homework Policy

You are encouraged to discuss ideas with other students. Nonetheless, every piece of work you turn in must be your own.
In each set a selected subset of problems will be graded and the emphasis will be put on checking
your thought process and clear exposition in addition to getting the numerical answers.
Do NOT assume the grader "knows the stuff, so will understand whatever you jot down", but make an
effort to write in a way so that your solutions are easy to follow.
It is your responsibility to make sure your homework is readable, that you communicate your solutions clearly. If the grader is unable to decipher what you have written, you might end up getting zero points for your homework set. So take care of your work. For example, state clearly the problem number;write in a logical order as opposed to "all over the place";include comments (if you make a calculation error, but your approach is correct you still get partial credit).
In addition, in order to be able to handle large volumes of papers and to return your homework within a reasonable time You need to STAPLE! If your homework is not stapled, it will NOT be accepted.
I will drop two of the lowest homework grades. So if you have to miss a homework assignment because of an emergency, then it can be dropped as the lowest grades. There is no credit for late homework

This syllabus is meant to be a tentative schedule for the semester.

Week Topic(s)/Sections Covered Homework DueDate
/Solution

Aug. 22
Introduction/1.3
Read the syllabus carefully!

Aug. 24
Directional Fields/1.1
(Today's office hour is 4-5 p.m. at UH2080B)
Sec1.3 (p24) 5, 6, 9, 12
Sec1.1 Do problem 3 and 4 in Extra homework (Click on it. You will see the assignment).
Aug. 26

Aug. 26
Separable equations/1.2, 2.2
Quiz
Sec1.1 Do problem 1 and 2 in Extra homework.
Sep. 2

Aug. 29
Separable equations/1.2, 2.2 Sec1.2 (p15) 1b, 2b (You have to show your work.)
Sep. 2

Aug. 31
Separable equations 2.2 Sec 2.2(p47) 7, 10, 14, 21, 30 Sep. 2

Sep. 2
First-order linear equations/ 2.1
Quiz
Sec 2.1( p39) 9, 10, (Just find the general solution and determine how solution behaves as t approaches infinity), 14, 31
Sep. 9

Sep. 5 Labor Day

Sep 6
Last date to drop

Sep. 7
Theorem on existence and uniqueness/2.4,
Sec 2.4(p75) 1, 4, 5,
Sep. 9

Sep. 9
Theorem on existence and uniqueness/2.4,
Quiz
Sec 2.4(p75) 7, 8, 14, 28
Sep. 16

Sep. 12
Autonomous equations/2.5
2.5(p88): 7, 9, 10, 13, 21 Sep. 16

Sep.14
Review and Catch up!

Sep. 16
First Midterm(in class)

Sep. 19
Exact equation /2.6
Sec 2.6 (p99) 3, 4, 10, 16
Sep 23

Sep. 21
Second order equation/3.1
Sec 3.1 (p142) 2, 8, 10, 21, 23, 24(Hint for 23 and 24: The solution
y=ce^(r1 t) + d e^(r2 t) converges to 0 as t approaches infinity if r1 < 0 and r2 < 0, The solution y=ce^(r1 t) + d e^(r2 t) is unbounded as t approaches infinity if r1 > 0 and r2>0.) Sep 23

Sep. 23
Fundamental Solutions; Wronskian; Linear Superposition/3.2
Quiz
Sec3.2 (p151) 9, 12, 13, 16 (Hint: Compute y(0) and y'(0).), 24, 25
Sep 30

Sep. 26
Linear Independence/3.3 Sec3.3 (p158) 15, 18, 24 Sep 30

Sep. 28
Complex roots & Characteristic equations/3.4 Sec3.3 (p158) 20
Sec3.4(p164) 8, 11, 18.
Sep 30

Sep. 30
Repeated roots/3.5

Sec3.4(p164) 27, 41, 42

Oct. 7

Oct. 3
Reduction of order/3.5
Euler equations /5.5
Method of Undetermined Coefficients/3.6
Quiz
Sec3.5(p172) 2, 12, 28, 37 Oct. 7

Oct. 5
Method of Undetermined Coefficients/3.6
Sec3.6(p184) 1, 6(Try y_p(t)= c t^2 e^(-t)) , 11, 12(Note that cosh(2t)= (e^(2t) + e^(-2t))/2. Try y_p(t)=cte^(2t) + d e^(-2t). )
Oct. 7

Oct. 7
Variations of Parameter, 3.7
Quiz
Sec3.6(p184) 2, 14, 17
Sec3.7(190) 3, 5, 6, 13, 14 Oct. 19

Oct. 10
Application, 3.9

Oct. 12
Review and Catch Up!

Oct. 14
Second Midterm
Last date to withdraw

Oct. 17
Fall Break

Oct. 19
Higher order equation 4.1 Sec 4.1 (p222) 3, 4, 6
Oct 28

Oct. 21
Higher order homogeneous equation 4.2
Quiz
Sec 4.2 (p230) 12, 14, 15, 22, 29(Just find the solution. You don't have to plot its graph.) Oct 28

Oct. 24
Nonhomogeneous higher order equation 4.3
Sec 4.3 (p235) 1, 4, 6 Oct 28

Oct. 26
Variation of Parameters, Laplace transform/4.4, 6.1 Sec 4.3 (p235) (Use the method ofAnnihilators to do the following problems. You need to show your work.) 13, 15, 17, 18 Oct 28

Oct. 28
Laplace transform 6.1
IW grade deadline
Quiz
Sec 6.1 Use table 6.2.1 on page 319 to find the Laplace transform of the following functions.
(a) 2t^2 + sin(2t) +e^t cos(2t)
(b) t e^(2t) - t e^t sin(2t)
Nov 4

Oct. 31
Initial value problem 6.2

Nov 4

Nov. 2
Initial value problem 6.2 Sec 6.2 (p 322) 12, 13, 18 Today's lecture note
Nov 4

Nov. 4
Initial value problem 6.2
Quiz
Sec 6.2 (p 322) 21, 23Today's lecture note

Nov 9

Nov. 7
Step functions, 6.3
Discontinuous forcing 6.4

Impulse functions 6.5
Sec 6.3(p330) 7, 8, 9, 10
Sec 6.4(p337) 1 (Just find the solution. You don't have to find the graph.)

Hint: There are two key formulae in these exercises.

(a) L(u_c(t)g(t-c))= e^{-cs} L(g(t))

(b) Given the foumula of g(t-c).
Then the formula of g(t)=g((t+c)-c).

In (8), Note that t^2-2t+2=(t-1)^2+1
f(t)=((t-1)^2+1)u_1(t)
Let g(t-1)=(t-1)^2+1. Then f(t)=u_1(t)g(t-1)
and g(t)=g((t+1) -1)= ((t+1)-1)^2+1=t^2+1.

In(9), Note that f(t)= (t- pi)( u_pi(t) - u_2pi(t)
= (t- pi) u_pi(t) - (t- pi)u_2pi(t)

Let g(t-pi)= t- pi and
h(t-2pi)= t- pi .

Then f(t)= u_pi(t) g(t-pi) - u_2pi(t) h(t-2pi),
g(t)=g((t+pi)-pi)= (t+pi)- p = t and
h(t)=h((t+2pi)-2pi)= (t+2pi)- pi=t+pi .

Finally L(f(t))
=L(u_pi(t) g(t-pi)) - L(u_2pi(t) h(t-2pi))
=e^{-pi s} L(g(t)) - e^{-2pi s} L(h(t)) .

Nov 9 Wednesday
(Note this is a special date)

Nov. 9
Impulse functions 6.5
Sec 6.4(p337) 5, 9 Today's lecture note
Note about step function
Sec 6.5(p337) 2, 3, 11
Hint: Use the formula L(delta(t-c))=e^{-cs}

Review problems
Nov 16 Wednesday
(Note this is a special date)

Nov. 11
Veterans Day!

Nov. 14
Convolutional integral 6.6

Nov. 16
Review and Catch up!

Nov. 18
Midterm III

Nov. 21
Convolutional integral 6.6 Sec6.6(p351)7, 9, 11, 14, 18, 26(Just use the Laplace transform to find the solution.)
Hint for 26: Note that L(int_0^t (t-z)f(z)dz)=L(t)L(f(t)).

s^3+1=(s+1)(s^2-s+1)=(s+1)((s-(1/2))^2+(3/4))

and 1/(s^3+1) = a/(s+1) + (c(s-(1/2))+b)/(s^2-s+1).

Dec. 2

Nov. 23
Thanksgivings!

Nov. 25
Thanksgivings!

Nov. 28
First Order Linear Equations, 7.4, 7.5

Sec7.5(p398)1, 5, 6 (Just find the solution.)
Dec. 2

Nov. 30
First Order Linear Equations, 7.5

Infomation about final exam

Dec. 2
First Order Linear Equations, 7.6
Quiz
1. Draw the trajectories of the solution and analyze the stability of origin in previoud hw (Sec7.5(p398)1, 5, 6.
You can just use the solution in the back of the book (p600) to do this problem.

Dec. 7
Wednesday
(Note this is a special date)

Dec. 5
First Order Linear Equations, 7.6

Sec7.6(p410) Find the solution, draw the trajectories of the solution,
and analyze the stability of origin in the following problems.
1, 2, 3, 9 Dec. 7
Wednesday
(Note this is a special date)

Dec, 7
First Order Linear system 7.8
Quiz
(Note this is a special date)
Sec7.8(p428) 1, 3, 7

Dec. 9
Nonlinear Equations Ch8

Dec. 14
Final Exam
10:15-12:15
Wednesday

|| Academic Calendar || University Final Exam Schedule

Week	Topic(s)/Sections Covered	Homework	DueDate /Solution
Aug. 22	Introduction/1.3	Read the syllabus carefully!
Aug. 24	Directional Fields/1.1 (Today's office hour is 4-5 p.m. at UH2080B)	Sec1.3 (p24) 5, 6, 9, 12 Sec1.1 Do problem 3 and 4 in Extra homework (Click on it. You will see the assignment).	Aug. 26
Aug. 26	Separable equations/1.2, 2.2 Quiz	Sec1.1 Do problem 1 and 2 in Extra homework.	Sep. 2
Aug. 29	Separable equations/1.2, 2.2	Sec1.2 (p15) 1b, 2b (You have to show your work.)	Sep. 2
Aug. 31	Separable equations 2.2	Sec 2.2(p47) 7, 10, 14, 21, 30	Sep. 2
Sep. 2	First-order linear equations/ 2.1 Quiz	Sec 2.1( p39) 9, 10, (Just find the general solution and determine how solution behaves as t approaches infinity), 14, 31	Sep. 9
Sep. 5	Labor Day
Sep 6	Last date to drop
Sep. 7	Theorem on existence and uniqueness/2.4,	Sec 2.4(p75) 1, 4, 5,	Sep. 9
Sep. 9	Theorem on existence and uniqueness/2.4, Quiz	Sec 2.4(p75) 7, 8, 14, 28	Sep. 16
Sep. 12	Autonomous equations/2.5	2.5(p88): 7, 9, 10, 13, 21	Sep. 16
Sep.14	Review and Catch up!
Sep. 16	First Midterm(in class)
Sep. 19	Exact equation /2.6	Sec 2.6 (p99) 3, 4, 10, 16	Sep 23
Sep. 21	Second order equation/3.1	Sec 3.1 (p142) 2, 8, 10, 21, 23, 24(Hint for 23 and 24: The solution y=ce^(r1 t) + d e^(r2 t) converges to 0 as t approaches infinity if r1 < 0 and r2 < 0, The solution y=ce^(r1 t) + d e^(r2 t) is unbounded as t approaches infinity if r1 > 0 and r2>0.)	Sep 23
Sep. 23	Fundamental Solutions; Wronskian; Linear Superposition/3.2 Quiz	Sec3.2 (p151) 9, 12, 13, 16 (Hint: Compute y(0) and y'(0).), 24, 25	Sep 30
Sep. 26	Linear Independence/3.3	Sec3.3 (p158) 15, 18, 24	Sep 30
Sep. 28	Complex roots & Characteristic equations/3.4	Sec3.3 (p158) 20 Sec3.4(p164) 8, 11, 18.	Sep 30
Sep. 30	Repeated roots/3.5	Sec3.4(p164) 27, 41, 42	Oct. 7
Oct. 3	Reduction of order/3.5 Euler equations /5.5 Method of Undetermined Coefficients/3.6 Quiz	Sec3.5(p172) 2, 12, 28, 37	Oct. 7
Oct. 5	Method of Undetermined Coefficients/3.6	Sec3.6(p184) 1, 6(Try y_p(t)= c t^2 e^(-t)) , 11, 12(Note that cosh(2t)= (e^(2t) + e^(-2t))/2. Try y_p(t)=cte^(2t) + d e^(-2t). )	Oct. 7
Oct. 7	Variations of Parameter, 3.7 Quiz	Sec3.6(p184) 2, 14, 17 Sec3.7(190) 3, 5, 6, 13, 14	Oct. 19
Oct. 10	Application, 3.9
Oct. 12	Review and Catch Up!
Oct. 14	Second Midterm Last date to withdraw
Oct. 17	Fall Break
Oct. 19	Higher order equation 4.1	Sec 4.1 (p222) 3, 4, 6	Oct 28
Oct. 21	Higher order homogeneous equation 4.2 Quiz	Sec 4.2 (p230) 12, 14, 15, 22, 29(Just find the solution. You don't have to plot its graph.)	Oct 28
Oct. 24	Nonhomogeneous higher order equation 4.3	Sec 4.3 (p235) 1, 4, 6	Oct 28
Oct. 26	Variation of Parameters, Laplace transform/4.4, 6.1	Sec 4.3 (p235) (Use the method ofAnnihilators to do the following problems. You need to show your work.) 13, 15, 17, 18	Oct 28
Oct. 28	Laplace transform 6.1 IW grade deadline Quiz	Sec 6.1 Use table 6.2.1 on page 319 to find the Laplace transform of the following functions. (a) 2t^2 + sin(2t) +e^t cos(2t) (b) t e^(2t) - t e^t sin(2t)	Nov 4
Oct. 31	Initial value problem 6.2		Nov 4
Nov. 2	Initial value problem 6.2	Sec 6.2 (p 322) 12, 13, 18 Today's lecture note	Nov 4
Nov. 4	Initial value problem 6.2 Quiz	Sec 6.2 (p 322) 21, 23Today's lecture note	Nov 9
Nov. 7	Step functions, 6.3 Discontinuous forcing 6.4 Impulse functions 6.5	Sec 6.3(p330) 7, 8, 9, 10 Sec 6.4(p337) 1 (Just find the solution. You don't have to find the graph.) Hint: There are two key formulae in these exercises. (a) L(u_c(t)g(t-c))= e^{-cs} L(g(t)) (b) Given the foumula of g(t-c). Then the formula of g(t)=g((t+c)-c). In (8), Note that t^2-2t+2=(t-1)^2+1 f(t)=((t-1)^2+1)u_1(t) Let g(t-1)=(t-1)^2+1. Then f(t)=u_1(t)g(t-1) and g(t)=g((t+1) -1)= ((t+1)-1)^2+1=t^2+1. In(9), Note that f(t)= (t- pi)( u_pi(t) - u_2pi(t) = (t- pi) u_pi(t) - (t- pi)u_2pi(t) Let g(t-pi)= t- pi and h(t-2pi)= t- pi . Then f(t)= u_pi(t) g(t-pi) - u_2pi(t) h(t-2pi), g(t)=g((t+pi)-pi)= (t+pi)- p = t and h(t)=h((t+2pi)-2pi)= (t+2pi)- pi=t+pi . Finally L(f(t)) =L(u_pi(t) g(t-pi)) - L(u_2pi(t) h(t-2pi)) =e^{-pi s} L(g(t)) - e^{-2pi s} L(h(t)) .	Nov 9 Wednesday (Note this is a special date)
Nov. 9	Impulse functions 6.5	Sec 6.4(p337) 5, 9 Today's lecture note Note about step function Sec 6.5(p337) 2, 3, 11 Hint: Use the formula L(delta(t-c))=e^{-cs} Review problems	Nov 16 Wednesday (Note this is a special date)
Nov. 11	Veterans Day!
Nov. 14	Convolutional integral 6.6
Nov. 16	Review and Catch up!
Nov. 18	Midterm III
Nov. 21	Convolutional integral 6.6	Sec6.6(p351)7, 9, 11, 14, 18, 26(Just use the Laplace transform to find the solution.) Hint for 26: Note that L(int_0^t (t-z)f(z)dz)=L(t)L(f(t)). s^3+1=(s+1)(s^2-s+1)=(s+1)((s-(1/2))^2+(3/4)) and 1/(s^3+1) = a/(s+1) + (c(s-(1/2))+b)/(s^2-s+1).	Dec. 2
Nov. 23	Thanksgivings!
Nov. 25	Thanksgivings!
Nov. 28	First Order Linear Equations, 7.4, 7.5	Sec7.5(p398)1, 5, 6 (Just find the solution.)	Dec. 2
Nov. 30	First Order Linear Equations, 7.5	Infomation about final exam
Dec. 2	First Order Linear Equations, 7.6 Quiz	1. Draw the trajectories of the solution and analyze the stability of origin in previoud hw (Sec7.5(p398)1, 5, 6. You can just use the solution in the back of the book (p600) to do this problem.	Dec. 7 Wednesday (Note this is a special date)
Dec. 5	First Order Linear Equations, 7.6	Sec7.6(p410) Find the solution, draw the trajectories of the solution, and analyze the stability of origin in the following problems. 1, 2, 3, 9	Dec. 7 Wednesday (Note this is a special date)
Dec, 7	First Order Linear system 7.8 Quiz (Note this is a special date)	Sec7.8(p428) 1, 3, 7
Dec. 9	Nonlinear Equations Ch8
Dec. 14	Final Exam 10:15-12:15 Wednesday