September 2

Homeworks III and IV are 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 substitutions (2:32)

1.6 Linear substitution example (6:12)

1.6 Homogeneous equations (4:41)

1.6 Homogeneous equation example (4:38)

Homework V due Sep 9

Section 1.5 Problems 34, 33,37

Section 1.6 Problems 3,18, 2,4,7,16

September 4

Videos to watch before class:

1.6 Bernoulli equations (3:30)

1.6 Bernoulli substitution example (8:57)

1.6 Exact differential equations (5:55)

1.6 Exact differential equation example (6:12)

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 Sep 9

Section 1.6 22,35,43,53,21,34,46,49,51

For 21-22 just reduce the differential equation to linear form

For 49,51,53 just reduce the differential equation to a first order equation.

The only problems that have to be solved completely are 34-35,43, 46

September 9

Test I

September 11

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

3.1 Constant coefficients example (7:33)

Homework VII due Sep 16

Section 3.1 2,17,25,27,33-34 (We ended up doing all the HW problems in class, so the grader will grade red HWs this assignment)

September 16

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 Higher order linear equations (7:00)

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)

Supplemental videos:

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

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

Homework VIII due Sep 23

Section 3.1 39, 40

Section 3.2 1,2,9,13,21,4,9,22,31(a)

September 18

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 IX due Sep 23

Section 3.3 15,24,26,27, 5,21,25,28,33

September 23

Homeworks VIII and IX due at the beginning of class.

Videos to watch before class:

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

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 Sep 30

Section 3.3 20,23,29,33,34 8,22,32 (32 isn't a complex root problem)

September 25

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 XI due Sep 30

Section 3.4 2,4,13,15, 1,3,18, 16-21 (except for 18, calculate if underdamped, overdamped or critically damped only)

Note: for problems 4,15,18, you don't have to write your solutions in the special form the book asks for.

September 30

Homeworks X and 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)

Homework XII due Oct 7

Section 3.5 6,21,32,43, 1,7,10,38

October 2

Videos to watch before class:

3.5 Variation of parameters (9:46)

3.5 Variation of parameters example (5:17)

3.5 Nonhomogeneous elliptic perpendicular pseudo-differential Euler-Lagrange wave equations (0:55)

Homework XIII due Oct 7

Section 3.5 21,47,57,63 48,51, 58,60

October 7

Homeworks XII and XIII due at the beginning of class.

Videos to watch before class:

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

3.6 Resonance(7:12)

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 Oct 14

Section 3.6 11,15,17,12,13 (You don't have to write the answer in the special form the book asks for),16,18,19,24

October 9

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 software here.

Homework XV due Oct 14

Section 4.1 2-5,12,14-15,18,20 (Just print out the PPLANE screenshot for 12 and 20)

All the homework problems were solved in class, so the grader might grade red problems this week.

October 14

Review for Test II

Homeworks XIV and XV due at the beginning of class.

October 16

Test II

October 21

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 differenital operators example (8:43)

Homework XVI due Oct 28

Section 4.2 2,6,13, 3,5,12,15,17

October 23

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 XVII due Oct 28

Section 3.8 2,3, 1,5,13

October 28

Homeworks XVI and XVII are due at the beginning of class

Videos to watch before class:

5.1 Matrix-valued functions (6:06)

5.1 Matrix equation example (3:55)

5.1 Principle of superposition for matrix-valued functions (2:53)

5.1 Linear independence example using Wronskians (3:12)

Homework XVIII due Nov 4

Section 5.1 11,14,22,26, 12,15,23,27,31-32,35-36

October 30

Videos to watch before class:

5.1 IVPs for matrix equations (3:54)

5.1 Elementary row operations (3:55)

5.1 IVP matrix example (2:53)

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)

Homework XIX due Nov 4

Section 5.1 35,39 ,38,40,

Section 7.1 1,5, 2,3

November 4

Homeworks XVIII and XIX are due at the beginning of class

Videos to watch before class:

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 Laplace transforms of step functions (4:12)

7.1 The Laplace transforms dictionary (4:54)

Homework XX due Nov 11

Section 7.1 11,13,16-17,19,23-29 12,14-15,18,20,31

November 6

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)

7.1 Existence of Laplace transforms (9:03)

7.3 Inverse Laplace transforms using simple partial fractions(2:16)

Homework XXI due Nov 11

Section 7.1 36,

Section 7.2 2,9, 17,20, 1,4,10,18-19,25

Additional questions:

Q1: Does e^{t^2} have a Laplace transform?

Q2: Does (e^{10t})^2 have a Laplace transform?

November 11

Homeworks XX and XXI are due at the beginning of class

Videos to watch before class:

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

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)

Homework XXII due Nov 18

Section 7.2 27(a), 28, 29,31, 27(b),30

Section 7.3 1,4-5,7,9,11,14, 2-3,5-6,8,12-13

November 13

Videos to watch before class:

7.3 Simple partial fractions review (2:47)

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

7.3 Partial fractions with irreducible factors review

7.3 Irreducible factors example (5:37)

Homework XXIII due Nov 18

Section 7.3 11,13,19,27,39 ,14,17,20,28,31,37

November 18

Videos to watch before class:

Homeworks XXII and XXIII are due at the beginning of 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)

Homework XXIV due Nov 25

Section 7.4 2,5,7,10,37, 1,6,8-9,36,38

November 20

Videos to watch before class:

7.4 Differentiation of Laplace transforms

7.4 Laplace transform differentiation example (2:44)

7.4 Integrals of Laplace transforms (5:09)

7.4 Laplace transform integration formula example (4:50)

Homework XXV due Nov 25

Section 7.4 15,17,20,29 16,18-19,21-22, 23,30, 31

November 25

Test III

Homeworks XX and XXI are due at the beginning of class

December 2

Review for Final

December 4

Review for Final