Classes

May 11

Homework I due May 12

Section 1.1 Problems 5,10,21-22,33,36

May 12

Homework I due at the beginning of class

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

1.2 Velocity problems

1.2 Acceleration problems

Homework II due May 13

Section 1.2 1,6,12,15,28,31

May 13

Homework II due at the beginning of class

Videos to watch before class:

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)

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 III due May 14

Section 1.3 6-8,11,13-15,22

Section 1.4 3,7,20 (use trig integral formulas in the front of your book)

May 14

Homework III due at the beginning of class

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)

1.5 Integrating factors (6:39)

1.5 Integrating factors IVP example (8:15)

Homework IV due May 15

Section 1.4 3,7,20,33,35

Section 1.5 10,12

May 15

Homework IV due at the beginning of class

Videos to watch before class:

1.5 Mixing problems (5:02)

1.5 Mixing problem example (10:17)

1.6 Linear substitution example (6:12)

1.6 Homogeneous equations (4:41)

1.6 Homogeneous equation example (4:38)

Homework V due May 18

Section 1.5 10,12,33,36

May 18

Homework V due at the beginning of class

Videos to watch before class:

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)

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 VI due May 19

Section 1.6 2,16,21,46,49

May 19

Homework VI due at the beginning of class

Midterm I today. Midterm will cover Sections 1.1-1.6.

May 20

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)

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

3.1 Constant coefficients example (7:33)

Homework VII due May 21

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

May 21

Homework VII due at the beginning of class

Videos to watch before class:

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)

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 VIII due May 22

Section 3.1. 34,36,40

Section 3.2 1,3,7,9,17,24,25

May 22

Homework VIII 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)

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

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

Homework IX due May 26

Section 3.1 44,45

Section 3.3 10,24,11, 26, 28,33,39

May 26

Homework IX due at the beginning of class

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 X due May 27

Section 3.3 9,20,22,30,36,40

May 27

Homework X due at the beginning of class

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)

Homework XI due May 28

Section 3.4 3,14,18,23. For 16-17,19-21 you only need to identify if the systems are overdamped, underdamped or critically damped. For 14a and 18, you do not have to write your solution in the cos(wt-a) form. .

May 28

Homework XI due at the beginning of class

Videos to watch before class:

3.5 Method of undetermined coefficients (2:52)

3.5 Undetermined coefficients polynomial example (2:05)

3.5 Undetermined coefficients trig example (5:00)

3.5 Matching coefficients (3:34)

Homework XII due May 29

Section 3.5 1,10,33,35

May 29

Homework XII due at the beginning of class

Videos to watch before class:

3.5 Variation of parameters (9:46)

3.5 Variation of parameters example (5:17)

3.6 Resonance(7:12)

Homework XIII due June 1

Section 3.5 52,59

Section 3.6 19-20

June 1

Homework XIII due at the beginning of class

Videos to watch before class:

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

3.6 Practical resonance example (4:07)

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 XIV due June 2

Section 3.6 4,12,16,18 (you don't have to write your answer in the cos(tw-a) form for any of these problems

June 2

Homework XIV due at the beginning of class

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 XV due June 3

Section 3.8 1,4,5 (only check for non-positive eigenvalues for 5)

June 3

Homework XV due at the beginning of class

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 XVI due June 5

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

June 4

Midterm II in PHSC 201

June 5

Homework XVI 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)

4.2 Higher order systems problem example (6:34)

Homework XVII due June 5

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

June 8

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 XVIII due June 9

Section 4.2 12,17,29

June 9

Homework XVIII 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)

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)

Homework XIX due June 10

Section 7.1 3,12,14-15,18-19

June 10

Homework XIX due today

Videos to watch before class

7.1 Existence of Laplace transforms (9:03)

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)

Homework XX due June 11

Section 7.1 23,25-27,29-30

Section 7.2 25,28, plus the following two questions:

Is e^(t^10) of exponential order?

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

June 11

Homework XX due today

Videos to watch before class

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)

7.2 Using Laplace transforms to solve IVP

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

Homework XXI due June 12

Section 7.2 1,4,8,10,18-21 (For 4,10 just find F(s)=L(x(t)): you don't have to find x(t))

June 12

Homework XXI due today

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 XXII due June 12

Section 7.2 6

Section 7.3 2-3,5-6,13,16-17 (Hint for 6- rewrite the numerator as (s+1)-2)

June 15

Homework XXII due today

Videos to watch before class:

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

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

Homework XXIII due June 16

Section 7.3 7-9,21,27,30,36

June 16

Homework XXIII 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 (optional)(9:43)

7.4 A convolution example (6:20)

7.4 Inverse Laplace transforms using convolution (2:31)

7.4 Application of convolution theorem (4:40)

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)

Homework XXIV due June 16

Section 7.4 5,8,11-14,36 Note: for 11-14, just write down the convolution product integral. Also solve the following additional problem:

Let x(t) be a function with x(0)=0. The Laplace transform of x(t) is denoted as F(s).

(a) Show that the Laplace transform of tx(t) is -F'(s), and that the Laplace transform of tx'(t) is -F(s)-sF'(s).

(b) What is the Laplace transform of tx''(t)? (You don't need to know the value of x'(0) to solve this problem!)

June 17

Homework XXIV due today

Videos to watch before class:

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)

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

Homework XXV due June 18

Section 7.4 15-16,31,32,33,34 (for 32 and 34, just find d/ds(ln(F(s))). For 33, you may assume that sin(t)*sin(t)=(1/2)(t cos t - sin t)

June 18

Homework XXV due today

Videos to watch before class:

Rewatch two videos from the previous class, plus one new one:

7.4 Integrals of Laplace transforms (5:09)

7.4 Laplace transform integration formula example (4:50)

7.1 Laplace transforms of step functions (4:12)

Homework XXVI due June 19

Section 7.1 7-8

Section 7.4 21,23,24

June 19

Homework XXVI due today

Videos to watch before class:

7.5 Piecewise functions

7.5 Piecewise functions example

Homework XXVII due June 23

Section 7.1 9

Section 7.5 2,3,8,11-12,20,31

June 22

Homework XXVII due today

Review for Chapter 1

June 24

Review for Chapter 3

June 25

Review for Chapter 4,7

June 26

Final