MATH 3113- Introduction to Ordinary Differential Equations, Sections 008 and 009 (2015 Spring Semester)

The syllabus for this course is here. Office hours are Wednesdsays 3:30-4:30 and Thursdays 2:00-3:00 in PHSC 1007.

Test 1 will be on Wednesday, February 4. Here is a sample test and last year's Test 1 is here. The only major difference is that we will not cover exact equations in our midterm 1.

Here are answers for Test 1 in the 008 section and in the 009 section.

Here are answers for Test 2 in the 008 section and in the 009 section.

Here are answers for Test 3 in the 008 section and in the 009 section.

Classes

January 14

Videos to watch before class:

1.1 Terminology

1.1 Modelling

1.2 General solutions of differential equations

1.2 Specific solutions of initial value problems

Homework I due Jan 23

Create an account on Math Stackexchange and earn the "informed" badge by taking the site tour. Write down your username on your homework.

Section 1.1 Problems 2,8,33-36

Section 1.2 Problems 3,4

January 16

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 I due Jan 23

Section 1.2 Problems 15,27-28

Section 1.3 Problems 21,22 (Graph these from x,y=-1,...,5. Sketch the curve, but ignore the part about finding y(-4)).

January 21

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 I due Jan 23

Section 1.3 Problems 12-16,23-24

Section 1.4 Problems 2,19

January 23

Videos to watch before class:

1.4 Separable equations (3:39)

1.4 Separable equations example (2:55)

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 Jan 30

Section 1.4 Problems 2,19,33,35,38

January 26

Videos to watch before class:

1.5 Integrating factors (6:39)

1.5 Integrating factors IVP example (8:15)

Homework II due Jan 30

Section 1.5 Problems 3,8,13

January 28

Videos to watch before class:

1.5 Mixing problems (5:02)

1.5 Mixing problem example (10:17)

Homework II due Jan 30

Section 1.5 Problems 33,36

January 30

Homework II due at the beginning of class.

Videos to watch before class:

1.6 Linear substitutions (2:32)

1.6 Linear substitution example (6:12)

1.6 Homogeneous equations (4:41)

1.6 Homogeneous equation example (4:38)

1.6 Bernoulli equations (3:30)

1.6 Bernoulli substitution example (8:57)

Homework III due Feb 6

Section 1.6 Problems 2,16,21

February 2

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 III due Feb 6

Section 1.6 Problems 46,49,51

February 4

Test I

Here is a sample test and last year's Test 1 is here. The only major difference is that we will not cover exact equations.

There will be additional office hours on Tuesday, February 3 5pm-6pm in PHSC 1007.

February 6

Homework III 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 (11:14)

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

Homework IV due Feb 13

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

February 9 (It's my BIRTHDAY!)

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 IV due Feb 13

Section 3.1. 34,36,40,44

Section 3.2 1,3,7,9

February 11

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 IV due Feb 13

Section 3.2 17,24,25,27

February 13

Homework IV due

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 V due Feb 20

Section 3.3 10,24,11, 26

February 16

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 V due Feb 20

Section 3.3 28,33,39

February 18

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 V due Feb 20

Section 3.3 9,20,22,36

February 20

Homework V due

Videos to watch before class:

3.4 Mass-spring models (10:48)

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

3.4 Identifying overdamped and underdamped systems (1:38)

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

Homework VI due Feb 27

Section 3.4 3,18, 16-21 (except for 18, calculate if underdamped, overdamped or critically damped only)

Note: for problem 18, you don't have to write your solutions in the special form the book asks for.

February 23

Videos to watch before class

3.6 An amplitude formula(5:04)

It might be helpful to review the other February 20 videos too

Homework VI due Feb 27

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

February 25

Videos to watch before class

3.5 Method of undetermined coefficients (2:52)

3.5 Undetermined coefficients polynomial example (2:05)

Homework VI due Feb 27

Section 3.5 1,35

February 27

Homework VI 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)

Homework VII due March 6

Section 3.5 38,51,63 (for 51 find the GENERAL solution, not just the PARTICULAR solution the book asks for)

March 2

Videos to watch before class

3.5 Matching coefficients (3:34)

3.6 Resonance(7:12)

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

3.6 Practical resonance example (4:07)

Homework VII due March 6

Section 3.6 16,18,19,20

March 4

SNOW DAY

March 6

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)

3.8 Introduction to endpoint problems (1:32)

Homework VIII due March 13

Section 3.6 12,13

March 9

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 VIII due March 13

Section 3.8 1,5

March 11

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.

No homework for this class

March 13

NO CLASS. I will prepare a video review for Midterm II instead. Hand in homework to the Math Dept office at PHSC 423

March 23

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 IX due March 27

Section 4.1 3-4,13,15,19. Remember to print out the PPLANE screenshot for 13,15,19. You only have to print out the PPLANE screenshot for 19.

March 25

Midterm 2

Study guide for Midterm 2

There will be additional office hours on Tuesday, March 24 5pm-6pm in PHSC 1007.

Principle of Superposition Review

Linear Independence Review

Constant Coefficients Review

Nonhomogeneous Equations Review

Unforced Spring Systems Review

Forced Spring Systems Review

March 27

Homework IX due at the beginning of class

Videos to watch before class

4.2 Elimination (3:40)

4.2 Elimination example (9:57)

4.2 Polynomial differential operators (4:48)

4.2 Polynomial differential operators example (8:43)

Homework X due April 3

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

March 30

Videos to watch before class

Rewatch two of Friday's videos, plus one new one:

4.2 Polynomial differential operators (4:48)

4.2 Polynomial differential operators example (8:43)

4.2 Higher order systems problem example (6:34)

Homework X due April 3

Section 4.2 12,17,48

April 1

Videos to watch before class

We didn't get to work out a problem related to the third video for Monday in class, so we'll do it today. Make sure you understand that example well.

4.2 Higher order systems problem example (6:34)

Homework X due April 3

Section 4.2 23-24,29

April 3

Homework X 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 XI due April 10

Section 7.1 3,12,14,19

April 6

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 XI due April 10

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

April 8

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 XI due April 10

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)?

April 10

Homework XI due today

I will be taking Good Friday off for religious reasons. The substitute instructor will give a lecture on solving initial value problems using Laplace transforms. Please try not to skip this lecture, since the topic today is the main point of chapter 7.

Homework XII due April 17

Section 7.2 1,4,5,8

April 13

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 XII due April 17

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

April 15

Videos to watch before class:

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

7.4 Differentiation of Laplace transforms (2:32)

7.4 Laplace transform differentiation example (2:44)

Helpful supplemental video:

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

Homework XII due April 17

Section 7.3 28,30

April 17

Homework XII due today

Videos to watch before class:

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 XIII due April 24

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

April 20

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 XIII due April 24

Section 7.4 15,16,21,23,25

April 22

Videos to watch before class:

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

Homework XIII due April 24

Section 7.4 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)

April 24

Midterm III

Homework XII due today

Office hours: Wednesday 3:30-4:30, Thursday 2pm-3pm

This midterm will cover sections 4.2, 7.1,7.2,7.3,7.4. Please make sure you understand all the Laplace transform techniques, including calculating a Laplace transform directly from its definition. You will not need to know the proofs of the techniques, other than the ones that follow immediately from integration by parts (i.e. 7.2 Theorem 1, 7.3 Theorem 1). Don't forget to study operational determinants too! As always, 90% of the test will be questions similar to your homework, and the last 10% will test your conceptual understanding of the material.

April 27- May 1

There will be reviews for the final during dead week. There will be no quiz. Attendance is optional, but recommended.