Dr. Peratt's M270 Homepage

Dr. Barry Peratt | 204 Gildemeister Hall | 507.457.5567 (Voice) | 507.457.5376 (Fax) | bperatt@winona.edu

MATH 270---DE's & LINEAR ALGEBRA
Fall Semester 2009

Course Materials Homepage | Math/Stat Homepage | Personal Homepage

ADMINISTRATIVE MATERIALS

HW & Date On Which to Work HW Description

Assignment 38
(11/17/2009) Complete the Homework on Creating Linear Transformations. Click here for the solutions.

Assignment 37
(11/16/2009) No New Homework.

Assignment 36
(11/13/2009)

Complete the Homework on Jordan Canonical Form. Click here for the solutions.

Study for Quiz #10 (see Assignment 33 below for details).

Assignment 35
(11/11/2009)

Complete the Homework on Linear Transformations. Click here for the solutions.

Study for Quiz #10, which will be given on Monday, 11/16/2009 and will cover the material from Assignments 31, 34, and 35.

Assignment 34
(11/10/2009)

Complete the Homework on Bases, Span, and Linear Independence. Click here for the solutions.

Section 4.3: 1-7 odd, 13, 16.

Section 4.4: 1, 3-5, 19, 24.

Assignment 33
(11/09/2009) No New Homework.

Assignment 32
(11/06/2009) No New Homework.

Assignment 31
(11/05/2009)

[Quiz #9]
[Solutions]

Complete the Homework on Matrix Arithmetic. Click here for the solutions.

Section 3.4: 1-11 odd, 31*.

Section 3.5: 1, 5.

Section 3.6: 1, 3.

Assignment 30
(10/30/2009)

Quiz #9 will be given on Tuesday, 11/03/2009 and will cover the material from Assignments 28-30.

Complete the Homework on RREF. Click here for solutions.

Section 3.1: 5, 13, 21, but instead of following the directions, (1) determine the number of objects and the dimension of the space in which they are embedded, (2) write an augmented matrix for the system of equations, (3) row-reduce the matrix on your TI-89, (4) write the vector and parametric forms of the solution and identify the dimension of the solution, and (5) identify a basis for the solution.

Section 3.3: 17, 19, 28. Repeat the instructions for Section 3.1 above.

Assignment 29
(10/29/2009) Section 3.3: 5, 7, 13.

Assignment 28
(10/27/2009) Complete the Homework on Parametric Functions.

Assignment 27
(10/19/2009)

The Project due date has been changed to Monday, 10/26/2009.

There is no class tomorrow, Tuesday, 10/20/2009 due to University Improvement Day.

I will arrive early (by 7:40 am) on Thursday for the test.

Assignment 26
(10/16/2009)

[Test #2]
[Solutions]

Project #1 will be due next Friday, 10/23/2009. We will have no more class days to work on it. On Monday, we will move on to the linear algebra portion of the course.

Test #2 will be given on Thursday, 10/22/2009 and will cover the material from Assignments 14-23.

Assignment 25
(10/13/2009)

[Quiz #8]
[Solutions]
Download and install WinPlot, which you will need to complete the bifurcation problem on the project.

Assignment 24
(10/12/2009)

Complete this problem on power series solutions to DEs (solution included).

There will be no quiz tomorrow, but Quiz #8 will be given on Thursday, 10/15/2009 and will cover the material from Assignments 21-24.

Assignment 23
(10/09/2009)

Continue working on Project #1. On Monday, we will cover series solutions of differential equations and then for the rest of the week we will work on the project in class.

Section 10.1: 2, 6.

Section 10.2: 4, 7, 10. Instead of finding the solution to the initial value problem, simply get to the point where we did in class; i.e. to the point where we know the LaPlace transform of the solution.

Mathematica: if on the above problems, you want to use Mathematica to find the solution by using the Inverse LaPlace Transform, here is the syntax:

LaplaceTransform[expression, t, s] --- to get the LaPlace transform of a function of t.

InvLaplaceTransform[expression, s, t] --- to get the Inverse LaPlace Transform of a function of s.

Maple: similar options are available for Maple, if you are interested:

with(inttrans): --- this loads the package you will need.

laplace(expression, t, s); ---to get the LaPlace Transform of a function of t.

invlaplace(expression, s, t); --- to get the Inverse LaPlace Transform of a function of s.

Assignment 22
(10/08/2009) Section 5.5: 9-12, 14, 16, 17-29 odd, 33, 36, 39.

Assignment 21
(10/06/2009)

[Quiz #7]
[Solutions]

Section 5.5: 1-4, 6, 13, 30, 35, 38, 40, 41.

Consider the forced (i.e. non-homogeneous) differential equation x''+4x'=29. Our Method of Undetermined Coefficients dictates that we guess x_p=a:

Try substituting this guess into the DE to make it work. What happens?

So, apparently, there is no solution to the forced DE of the form x_p=a. Why is this? (Look at the solution to the homogeneous equation).

Download Project #1.

Assignment 20
(10/05/2009) Study for Quiz #7, which will be given tomorrow, Tuesday 10/06/2009 and will cover the material in Assignments 16, 18, and 19.

Assignment 19
(10/02/2009) Section 5.3: 5, 7, 10, 11, 12, 13, 15, 16, 19, 25, 32.

Assignment 18
(10/01/2009) Section 5.3: 6, 8, 14, 17, 23, 30.

Assignment 17
(9/29/2009)

[Quiz #6]
[Solutions]
No New Homework.

Assignment 16
(9/28/2009)

Study for Quiz #6, which will be given on Tuesday, 9/29/09 and will cover the material from Assignments 14 and 15.

Section 5.3: 1-4, 21, 24.

Download an explanation of Problem #11 in Section 1.5.

Assignment 15
(9/25/2009)

[Test #1]
[Solutions]
Section 1.5: 1-25 every other odd, 30. On these assignments, use the Integrating Factor to make the DE separable (but you may use the TI-89 to perform the integration).

Assignment 14
(9/18/2009)

Study for Test #1, which will be given on Monday, 9/21/2009 and will cover the material from Assignments 2-13.

The following homework is technically Monday night's homework. There will be no quiz on Tuesday.

Section 1.4: 1-27 every odd (or every other odd, depending on how much practice you feel you need), 29-31, 32*.

Section 2.1: 4, 8, 9, 10, 12, 29, 30.

Assignment 13
(9/17/2009)

Complete the Homework on Classifying DE's. Click here for the solutions.

The homework on population models will have to wait until we cover some analytic techniques.

Remember that Test #1 will be administered on Monday, 9/21/2009 and will cover the material up to and including the homework from Thursday, 9/17/2009.

Assignment 12
(9/15/2009)

[Quiz #5]
[Solutions]

No New Homework.

Test #1 will be administered on Monday, 9/21/2009 and will cover the material up to and including the homework from Thursday, 9/17/2009.

Assignment 11
(9/14/2009) Study for Quiz #5, which will be given tomorrow, Tuesday, 9/15/2009 and will cover the material from Assignments 9 and 10.

Assignment 10
(9/11/2009)

[Quiz #4]
[Solutions]

Complete the Homework on Bifurcations (click here for the solutions).

If time permits, begin working on Section 2.2: 19-22, 29. For problems 19-21, in addition to following the directions in the book, also sketch the bifurcation diagrams. This material will not appear on Tuesday's quiz but will be assigned again on Monday night.

Assignment 9
(9/08/2009)

Study for Quiz #4, which will be given on Thursday, 9/10/2009 and will cover the material from Assignments 5-8.

Section 2.2: 1-17 odd, but instead of following the directions, simply (1) identify the equlibrium points, (2) plot the phase diagram, correctly indicating the nature of each equilibrium point, (3) sketch a plot of the time series (i.e. y vs. t), and (4) indicate the different regimes of behavior.

Complete the Practice on Qualitative Analysis. (Click here for the solutions.)

Assignment 8
(9/04/2009) Section 1.3: 11-20.

Assignment 7
(9/03/2009) No New Homework.

Assignment 6
(9/01/2009)

[Quiz #3]
[Solutions]
Section 2.4: 1, 3, 5, 9, 25*. (Note that the "limiting velocity" is by definition that velocity v that, when reached, results in a zero rate of change---i.e. the velocity at which the object "gets stuck" and doesn't accelerate any more.)

Assignment 5
(8/31/2009)

Study for Quiz #3, which will be given tomorrow, Tuesday 9/01/2009 and will cover the material in Assignments 2-4.

Complete this Practice on Particular Solutions.

Section 1.3: 1-9 odd.

Assignment 4
(8/28/2009)

Section 1.1: 37-43 all (these are very important conceptual questions).

Section 1.2: 1-17 odd, 19-22.

Assignment 3
(8/27/2009)

In class, we developed a DE for a linear oscillator and found, in particular, that:

Force of the spring satisfies F=-kx. What factors affect the value of k?

Force of friction satisfies F=-bx. What factors affect the value of b?

Verify that x=Ae^t+Be^-3t is a solution to the DE x''+2x'-3x=0. Given the initial conditions x(0)=3 and x'(0)=1, find the particular solution. (Answer: x=2.5e^t+0.5e^-3t)

Section 1.1: 1-11 odd, 17-25 odd (disregard the directions about graphing the solutions).

Assignment 2
(8/25/2009) Complete the Homework on Modeling---Part 1 (solutions are included).

Assignment 1
(8/24/2009)

Complete the Personal Profile Survey by Tuesday 8/25/2009. This will count as Quiz #1 (0% if you don't complete it, 100% otherwise). But, read the next bullet before completing the survey.

Carefully read through your syllabus. In it you will find embedded words that very clearly do not belong. In the appropriate box on the Personal Profile Survey, list all of the words that don't belong in the syllabus. This will count as Quiz #2.

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Page last updated on: 04/27/2008 09:58:01 AM

HW & Date On Which to Work	HW Description
Assignment 38 (11/17/2009)	Complete the Homework on Creating Linear Transformations. Click here for the solutions.
Assignment 37 (11/16/2009)	No New Homework.
Assignment 36 (11/13/2009)	Complete the Homework on Jordan Canonical Form. Click here for the solutions. Study for Quiz #10 (see Assignment 33 below for details).
Assignment 35 (11/11/2009)	Complete the Homework on Linear Transformations. Click here for the solutions. Study for Quiz #10, which will be given on Monday, 11/16/2009 and will cover the material from Assignments 31, 34, and 35.
Assignment 34 (11/10/2009)	Complete the Homework on Bases, Span, and Linear Independence. Click here for the solutions. Section 4.3: 1-7 odd, 13, 16. Section 4.4: 1, 3-5, 19, 24.
Assignment 33 (11/09/2009)	No New Homework.
Assignment 32 (11/06/2009)	No New Homework.
Assignment 31 (11/05/2009) [Quiz #9] [Solutions]	Complete the Homework on Matrix Arithmetic. Click here for the solutions. Section 3.4: 1-11 odd, 31. Section 3.5:* 1, 5. Section 3.6: 1, 3.
Assignment 30 (10/30/2009)	Quiz #9 will be given on Tuesday, 11/03/2009 and will cover the material from Assignments 28-30. Complete the Homework on RREF. Click here for solutions. Section 3.1: 5, 13, 21, but instead of following the directions, (1) determine the number of objects and the dimension of the space in which they are embedded, (2) write an augmented matrix for the system of equations, (3) row-reduce the matrix on your TI-89, (4) write the vector and parametric forms of the solution and identify the dimension of the solution, and (5) identify a basis for the solution. Section 3.3: 17, 19, 28. Repeat the instructions for Section 3.1 above.
Assignment 29 (10/29/2009)	Section 3.3: 5, 7, 13.
Assignment 28 (10/27/2009)	Complete the Homework on Parametric Functions.
Assignment 27 (10/19/2009)	The Project due date has been changed to Monday, 10/26/2009. There is no class tomorrow, Tuesday, 10/20/2009 due to University Improvement Day. I will arrive early (by 7:40 am) on Thursday for the test.
Assignment 26 (10/16/2009) [Test #2] [Solutions]	Project #1 will be due next Friday, 10/23/2009. We will have no more class days to work on it. On Monday, we will move on to the linear algebra portion of the course. Test #2 will be given on Thursday, 10/22/2009 and will cover the material from Assignments 14-23.
Assignment 25 (10/13/2009) [Quiz #8] [Solutions]	Download and install WinPlot, which you will need to complete the bifurcation problem on the project.
Assignment 24 (10/12/2009)	Complete this problem on power series solutions to DEs (solution included). There will be no quiz tomorrow, but Quiz #8 will be given on Thursday, 10/15/2009 and will cover the material from Assignments 21-24.
Assignment 23 (10/09/2009)	Continue working on Project #1. On Monday, we will cover series solutions of differential equations and then for the rest of the week we will work on the project in class. Section 10.1: 2, 6. Section 10.2: 4, 7, 10. Instead of finding the solution to the initial value problem, simply get to the point where we did in class; i.e. to the point where we know the LaPlace transform of the solution. Mathematica: if on the above problems, you want to use Mathematica to find the solution by using the Inverse LaPlace Transform, here is the syntax: LaplaceTransform[expression, t, s] --- to get the LaPlace transform of a function of t. InvLaplaceTransform[expression, s, t] --- to get the Inverse LaPlace Transform of a function of s. Maple: similar options are available for Maple, if you are interested: with(inttrans): --- this loads the package you will need. laplace(expression, t, s); ---to get the LaPlace Transform of a function of t. invlaplace(expression, s, t); --- to get the Inverse LaPlace Transform of a function of s.
Assignment 22 (10/08/2009)	Section 5.5: 9-12, 14, 16, 17-29 odd, 33, 36, 39.
Assignment 21 (10/06/2009) [Quiz #7] [Solutions]	Section 5.5: 1-4, 6, 13, 30, 35, 38, 40, 41. Consider the forced (i.e. non-homogeneous) differential equation x''+4x'=29. Our Method of Undetermined Coefficients dictates that we guess x_p=a: Try substituting this guess into the DE to make it work. What happens? So, apparently, there is no solution to the forced DE of the form x_p=a. Why is this? (Look at the solution to the homogeneous equation). Download Project #1.
Assignment 20 (10/05/2009)	Study for Quiz #7, which will be given tomorrow, Tuesday 10/06/2009 and will cover the material in Assignments 16, 18, and 19.
Assignment 19 (10/02/2009)	Section 5.3: 5, 7, 10, 11, 12, 13, 15, 16, 19, 25, 32.
Assignment 18 (10/01/2009)	Section 5.3: 6, 8, 14, 17, 23, 30.
Assignment 17 (9/29/2009) [Quiz #6] [Solutions]	No New Homework.
Assignment 16 (9/28/2009)	Study for Quiz #6, which will be given on Tuesday, 9/29/09 and will cover the material from Assignments 14 and 15. Section 5.3: 1-4, 21, 24. Download an explanation of Problem #11 in Section 1.5.
Assignment 15 (9/25/2009) [Test #1] [Solutions]	Section 1.5: 1-25 every other odd, 30. On these assignments, use the Integrating Factor to make the DE separable (but you may use the TI-89 to perform the integration).
Assignment 14 (9/18/2009)	Study for Test #1, which will be given on Monday, 9/21/2009 and will cover the material from Assignments 2-13. The following homework is technically Monday night's homework. There will be no quiz on Tuesday. Section 1.4: 1-27 every odd (or every other odd, depending on how much practice you feel you need), 29-31, 32. Section 2.1:* 4, 8, 9, 10, 12, 29, 30.
Assignment 13 (9/17/2009)	Complete the Homework on Classifying DE's. Click here for the solutions. The homework on population models will have to wait until we cover some analytic techniques. Remember that Test #1 will be administered on Monday, 9/21/2009 and will cover the material up to and including the homework from Thursday, 9/17/2009.
Assignment 12 (9/15/2009) [Quiz #5] [Solutions]	No New Homework. Test #1 will be administered on Monday, 9/21/2009 and will cover the material up to and including the homework from Thursday, 9/17/2009.
Assignment 11 (9/14/2009)	Study for Quiz #5, which will be given tomorrow, Tuesday, 9/15/2009 and will cover the material from Assignments 9 and 10.
Assignment 10 (9/11/2009) [Quiz #4] [Solutions]	Complete the Homework on Bifurcations (click here for the solutions). If time permits, begin working on Section 2.2: 19-22, 29. For problems 19-21, in addition to following the directions in the book, also sketch the bifurcation diagrams. This material will not appear on Tuesday's quiz but will be assigned again on Monday night.
Assignment 9 (9/08/2009)	Study for Quiz #4, which will be given on Thursday, 9/10/2009 and will cover the material from Assignments 5-8. Section 2.2: 1-17 odd, but instead of following the directions, simply (1) identify the equlibrium points, (2) plot the phase diagram, correctly indicating the nature of each equilibrium point, (3) sketch a plot of the time series (i.e. y vs. t), and (4) indicate the different regimes of behavior. Complete the Practice on Qualitative Analysis. (Click here for the solutions.)
Assignment 8 (9/04/2009)	Section 1.3: 11-20.
Assignment 7 (9/03/2009)	No New Homework.
Assignment 6 (9/01/2009) [Quiz #3] [Solutions]	Section 2.4: 1, 3, 5, 9, 25*. (Note that the "limiting velocity" is by definition that velocity v that, when reached, results in a zero rate of change---i.e. the velocity at which the object "gets stuck" and doesn't accelerate any more.)
Assignment 5 (8/31/2009)	Study for Quiz #3, which will be given tomorrow, Tuesday 9/01/2009 and will cover the material in Assignments 2-4. Complete this Practice on Particular Solutions. Section 1.3: 1-9 odd.
Assignment 4 (8/28/2009)	Section 1.1: 37-43 all (these are very important conceptual questions). Section 1.2: 1-17 odd, 19-22.
Assignment 3 (8/27/2009)	In class, we developed a DE for a linear oscillator and found, in particular, that: Force of the spring satisfies F=-kx. What factors affect the value of k? Force of friction satisfies F=-bx. What factors affect the value of b? Verify that x=Ae^t+Be^-3t is a solution to the DE x''+2x'-3x=0. Given the initial conditions x(0)=3 and x'(0)=1, find the particular solution. (Answer: x=2.5e^t+0.5e^-3t) Section 1.1: 1-11 odd, 17-25 odd (disregard the directions about graphing the solutions).
Assignment 2 (8/25/2009)	Complete the Homework on Modeling---Part 1 (solutions are included).
Assignment 1 (8/24/2009)	Complete the Personal Profile Survey by Tuesday 8/25/2009. This will count as Quiz #1 (0% if you don't complete it, 100% otherwise). But, read the next bullet before completing the survey. Carefully read through your syllabus. In it you will find embedded words that very clearly do not belong. In the appropriate box on the Personal Profile Survey, list all of the words that don't belong in the syllabus. This will count as Quiz #2.