Homework I due August 28

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Section 1.1 Problems 2,8,21-22 (remember to sketch!) 33,36

Section 1.2 Problems 3,4

Here are Sections 1.1 and 1.2 from your book. I will not provide the textbook scans for future weeks, so please have the textbook by then!

August 28

Homework I due today

Videos to watch before class:

1.2 Velocity problems

1.2 Acceleration problems

1.3 Slope fields (8:23)

1.3 Slope field applet (3:09)

The link to the slope field applet in the above video is here.

If your computer doesn't like the security settings of the file and you don't know how to fix the problem, try this applet instead.

1.3 Sketching solutions of initial value problems(2:11)

Homework II due Sept 4

Section 1.2 Problems 12,15,28,31

Section 1.3 Problems 6-8,22

August 31

Videos to watch before class:

1.3 Sketching solutions of initial value problems(2:11)

1.3 Existence-uniqueness principle (3:51)

1.3 Existence-uniqueness example (4:43)

1.4 Separable equations (3:39)

1.4 Separable equations example (2:55)

Homework II due Sep 4

Section 1.3 6-8,11,13-14,22. Also do #15, except replace sqrt(x-y) with ln(x-y).

Section 1.4 3,7

September 2

Videos to watch before class:

1.4 The growth/decay equation (7:18)

1.4 Growth/decay equation example (7:29)

1.4 Population growth example (6:26)(optional)

Homework II due Sep 4

Section 1.4 20,33,35

September 4

Homework II due at the beginning of class

Videos to watch before class:

1.5 Integrating factors (6:39)

1.5 Integrating factors IVP example (8:15)

Homework III due Sep 11

Section 1.5 3,8,13

September 9

1.5 Mixing problems (5:02)

1.5 Mixing problem example (10:17)

Homework III due Sep 11

Section 1.5 33,36

September 11

Homework III due at the beginning of class

Please read this article. There is a chance that the quiz will be on this rather than on the videos!

1.6 Linear substitution example (6:12)

1.6 Homogeneous equations (4:41)

1.6 Homogeneous equation example (4:38)

Homework IV due Sep 18

Section 1.6 Problems 2,16,21

Septmeber 14

Videos to watch before class:

1.6 Bernoulli equations (3:30)

1.6 Bernoulli substitution example (8:57)

1.6 Reducible second order equations (4:50)

1.6 Reducible second order example with no y (5:16)

1.6 Reducible second order example with no x (4:49)

Homework IV due Sep 18

Section 1.6 Problems 46,49. In addition, please perform the appropriate u-substitution for 6,7,19,53. You don't have to solve those problems completely.

September 16

Midterm Test I

Extra office hours Tuesday 5-6pm

You may consult the web pages of my previous diff eq sections to look at past tests, by clicking on the "Teaching" tab on top of the page.

September 18

Homework IV due at the beginning of class

Videos to watch before class:

3.1 Second order linear differential equations (7:10)

3.1 The principle of superposition (8:06)

3.1 Existence-uniqueness principle for second order linear ODEs (3:56) (Optional)

3.1 Linearly independent functions (4:52)

3.1 General solutions for second order linear ODEs (8:13)

3.1 Wronskians and general solutions (4:12)

3.1 Finding a particular solution for a second order ODE (4:34)

Homework V due Sep 25

Section 3.1 6,12,17,21,27,30

Septmeber 21

Videos to watch before class:

3.1 Second order linear homogeneous ODes with constant coefficients (4:20)

3.1 Constant coefficients example (7:33)

3.1 When the characteristic polynomial has a repeated root (2:38)

3.1 Repeated roots example (3:03)

3.2 Double root explanation (7:51) (optional)

3.2 Higher order linear equations (7:00) (Everything after the 4:00 mark is optional)

3.2 Linear independence and Wronskians for n functions (6:42)

3.2 Linear (in)dependence exmaples (8:42)

Homework V due Sep 25

Section 3.1. 34,36,40,44

Section 3.2 1,3,7,9

Septmeber 23

Videos to watch before class:

3.2 General solutions for second order linear equations (4:01)

3.2 Example for finding a general solution for an inhomogeneous equation (3:43)

3.2 Linear dependence by calculating constants example (3:44)

Homework V due Sep 25

Section 3.2 17,24,25,27

Septmeber 25

Videos to watch before class:

Homework V due at the beginning of class

Videos to watch before class:

3.3 Homogeneous equations with constant coefficients (3:23)

3.3 Distinct real roots example (8:39)

3.3 Repeated real roots (3:13)

3.3 Repeated real root example (2:44)

Homework VI due Oct 2

Section 3.3 10,24,11, 26

September 28

Videos to watch before class:

Algebra review: Polynomial long division (2:59) (optional)

Solving a problem when knowing one root of the characteristic polynomial (2:04)

Homework VI due Oct 2

Section 3.3 28,33,39

September 30

Videos to watch before class:

3.3 Characteristic equations with complex roots (6:30)

3.3 Complex root example (2:00)

3.3 Repeated complex roots example (3:42)

Homework VI due Oct 2

Section 3.3 9,20,22,36

October 2

Homework VI due

Videos to watch before class:

3.4 Mass-spring models (10:48)

3.4 Undamped mass-spring motion example (7:26)

Homework VII due Oct 12

Section 3.4 2-3 (to find the amplitude, you might have to watch the Oct 5 videos)

October 5

Videos to watch before class:

3.4 Identifying overdamped and underdamped systems (1:38)

3.6 An amplitude formula(5:04)(optional)

Homework VII due Oct 12

Section 3.4 14,18,23 (for 14(a) and 18, you don't have to write the solution in that special cos(wt-a) form)

Additionally, for 16-17,19-21 just write down if the system is overdamped, underdamped, or critically damped.

October 7

Videos to watch before class

3.5 Method of undetermined coefficients (2:52)

3.5 Undetermined coefficients polynomial example (2:05)

Homework VII due Oct 12

Section 3.5 1,35

October 12

Homework VII due

Videos to watch before class

3.5 Undetermined coefficients trig example (5:00)

3.5 Variation of parameters (9:46)

3.5 Variation of parameters example (5:17)

3.5 Matching coefficients (3:34)

Homework VIII due Oct 16

Section 3.5 38,51,63

October 14

Videos to watch before class

3.6 Resonance(7:12)

3.6 Damped forced oscillations and practical resonance (9:12)

3.6 Practical resonance example (4:07)

Homework VIII due Oct 16

Section 3.6 16,18,19,20

OCtober 16

Homework VIII due today

Videos to watch before class

3.6 Steady periodic and transient solutions (2:48)

3.6 Transient and steady periodic solutions example Part 1 (8:14)

3.6 Transient and steady periodic solutions example Part 2 (5:48)

Homework IX due Oct 23

Section 3.6 12,13 (you don't have to write your solution in the cos(wt-a) form the book wants)

OCtober 19

Videos to watch before class

3.8 Introduction to endpoint problems (1:32)

3.8 Eigenvalues (6:36)

3.8 Eigenvalue example I (8:29)

3.8 Eigenvalue example II (5:15)

Homework IX due Oct 23

Section 3.8 1,5

October 21

Videos to watch before class

4.1 Systems of ODEs introduction (2:38)

4.1 Reducing a higher order DE to a system (4:21)

4.1 PPLANE tutorial (4:23)

Download the PPLANE java applet here.

We will also work out a short 3.8 problem, so it might be good to rewatch the March 9 videos.

Homework X due Oct 30

Section 4.1 3-4,13,15 (4th edition book numbering might be different for this chapter)

October 23

Homework IX due today

Videos to watch before class

4.1 Systems of ODEs introduction (2:38)

4.1 Reducing a higher order DE to a system (4:21)

4.1 Solving simple systems (1:34)

4.1 Simple systems example (5:40)

4.1 PPLANE tutorial (4:23)

Download the PPLANE java applet here.

Homework X due Oct 30

Section 4.1 3-4,13,15,19. You only have to print out the PPLANE screenshot for 19. 4th edition book numbering might be different for this chapter

October 26

We will continue with the material in Section 4.1. There will also be a review for the test in the remaining time

October 28

There will be additional office hours on Tuesday, October 27 5pm-6pm in PHSC 1007 for the test on Wednesday.

Principle of Superposition Review

Linear Independence Review

Constant Coefficients Review

Nonhomogeneous Equations Review

Unforced Spring Systems Review

Forced Spring Systems Review

October 30

Homework X due at the beginning of class

Videos to watch before class

4.2 Elimination (3:40)

4.2 Elimination example (9:57)

Homework XI due November 6

Section 4.2 3,5,7 (You don't have to bother with the graphing)

For the 002 class only: also show that P(x)y''(x)+Q(x)y'(x)+R(x)y(x)=0 obeys the superposition principle even when P(x), Q(x), R(x) contain x terms.

That is, given solutions y_1(x),y_2(x) show that C_1y_1(x)+C_2y_2(x) is also a solution.

November 2

Videos to watch before class

4.2 Polynomial differential operators (10:50)

4.2 Polynomial differential operators example (9:52)

Homework XI due November 6

Section 4.2 12,17

November 4

Videos to watch before class

4.2 Differential operators with nonhomogeneous systems

Homework XI due November 6

Section 4.2 7,26,29

November 6

Homework XI due today

Videos to watch before class

7.1 Laplace transform introduction (2:28)

7.1 Laplace transforms of constant functions (2:19)

7.1 Laplace transforms of exponential functions (2:25)

7.1 The Gamma function (1:54)

7.1 Gamma(1)=1 (1:11)

7.1 Gamma(x+1)=xGamma(x) (4:19)

7.1 Laplace transforms of power functions (2:20)

Homework XII due November 13

Section 7.1 3,12,14,19

November 9

Videos to watch before class

7.1 Linearity of Laplace transforms (2:10)

7.1 Laplace transforms of trig and hyperbolic trig functions (5:34)

7.1 The Laplace transforms dictionary (4:54)

7.1 Inverse Laplace transforms example (4:06)

7.1 Existence of Laplace transforms (9:03)

Homework XII due November 13

Here is the Laplace Transform formula sheet

Section 7.1 15,18-19,23,25-27,29-30

November 11

Videos to watch before class

7.2 Laplace transforms of derivatives (4:32)

7.2 Laplace transforms of higher derivatives (2:15)

7.2 Laplace transforms using the product rule (2:35)

7.2 Laplace transforms of integrals (2:07)

7.2 Laplace transform integral rule example (2:46)

7.2 Inverse Laplace transform integral rule example (6:24)

Homework XII due November 13

Section 7.2 18-21,25,28, plus the following two questions.

Does e^(t^10) have a Laplace transform?

How about (e^t)^(10)?

November 13

Homework XII due today

Videos to watch before class

7.2 Using Laplace transforms to solve IVPs

(Note: the second initial condition should be x'(0)=2, not x''(0)=2)

Homework XIII due November 20

Section 7.2 1,4,8

November 16

Videos to watch before class:

7.3 Translations of the s variable(2:07)

7.3 Laplace transform example using s translation (2:28)

7.3 Simple partial fractions review (2:47)

7.3 Inverse Laplace transforms using simple partial fractions (2:17)

7.3 Inverse Laplace transform example using partial fractions (6:26)

Homework XIII due November 20

Section 7.3 2-3,5-6,13,16-17

November 18

Videos to watch before class:

7.3 Initial Value Problems using partial fractions and inverse Laplace transforms(5:35)

Helpful supplemental video:

7.4 Inverse Laplace transforms by completing the square (6:01)

Homework XIII due November 20

Section 7.3 28,30

November 20

Homework XIII due today

Videos to watch before class:

7.4 Differentiation of Laplace transforms (2:32)

7.4 Laplace transform differentiation example (2:44)

7.4 Introduction to the convolution product (2:58)

7.4 Order of the convolution product doesn't matter (3:38)

7.4 The convolution property (9:43)

7.4 A convolution example (6:20)

7.4 Inverse Laplace transforms using convolution (2:31)

Helpful supplemental video:

7.4 Application of convolution theorem (4:40)

Homework XIV due November 30

Note: for 11-14, just write down the convolution product integral. You don't have to solve the integral. For 36, please watch the supplemental video.

Section 7.4 5,8,11-14,36

November 23

Videos to watch before class:

7.4 Differentiation of Laplace transforms (2:32)

7.4 Laplace transform differentiation example (2:44)

7.4 Finding inverse Laplace transforms using the derivative formula (5:58)

7.4 Integrals of Laplace transforms (5:09)

7.4 Laplace transform integration formula example (4:50)

Homework XIV due November 30

Section 7.4 15,16,21,23,25

November 30

Homework XIV due today

Videos to watch before class:

7.4 Laplace transforms of Logarithms

7.4 IVP using the differentiation and integration formulas (6:41)

Homework XV due December 7

Section 7.4 23,25,31,32,33,34 (for 32 and 34, just find d(ln(X(s))/ds). For 33, you may assume that sin(t)*sin(t)=(1/2)(t cos t - sin t)

December 2

PLEASE BRING LAPTOP OR OTHER COMPUTING DEVICE TODAY

Videos to watch before class:

7.4 IVP using the differentiation and integration formulas (6:41)

December 4

Midterm 3. The midterm will cover Sections 4.2,7.1,7.2,7.3,7.4.

Office hours on Thursday December 5: 1-3pm, and 5-6pm.

December 7

Homework XV due today

Chapter 1 review

December 9

Chapter 3 + 4.1 review

December 11

Chapter 7 + 4.2 review