### Updates/Revisions to the Math 252 Course Webpages

- I've modified the timeline to add an extra online session for Section 6.2. See the Study Plan below (or the Pacing Schedule on the About page) for details.
- DX02 (Mech): Test 3 has been moved to the following week. The DX01 (Civil) section writes on the original date. Please note that the sections covered have changed. See the Tests page for details.

### Links to other Math 252 Sites

- You can find more resources on the Math 252 websites for the following
Camosun instructors:
- Gilles Cazelais:
- Course Notes and Resources page
- Math 252 main page, which has practice questions under the Homework heading and handouts at the bottom of the page

- Leah Howard's site has some old Math 252 tests.

- Gilles Cazelais:
- (You'll find some redundancy because we do share resources.)

### Study Plan

#### Week 1: Jan 11 to Jan 15

- Section 1.1: Definitions and Terminology
- My lecture notes – these are skeleton notes from last year's lecture class. For more detailed notes, please check out Gilles Cazelais' Math 252 Course Notes Page.
- Handout: Definitions

- Section 1.2: Initial-Value Problems
- Section 2.2: Separable Variables
- WeBWorK Assign0, which is due the following week

#### Week 2: Jan 18 to Jan 22

- Section 2.3: Linear Equations
- Section 2.5: Solutions by Substitutions (we're doing this section before 2.4)
- WeBWorK Assign1, which is due the following week

#### Week 3: Jan 25 to Jan 29

- Section 2.4: Exact Equations
- Chapter 2 Review:
- Steps to Determine Type of DE
- Name that DE! practice sheet

- Section 3.1: Linear Models
- Fun link of the week: Mad Engineers

#### Week 4: Feb 1 to Feb 5

- Finish up 3.1.

**Test 1 covers the material up to this point**.

- Section 4.1: Preliminary Theory - Linear Equations
- Section 4.2: Reduction of Order
- Section 4.3: Homogeneous Linear Equations with Constant Coefficients
- My lecture notes
- Handout: Explainer on Methodology
- Handout: Explainer on Complex Solutions
- Handout: Susie's Handout on Higher Order Homogeneous DEs
- Handout: Graphs of Solutions and Annotated Version

#### Week 5: Feb 8 to Feb 12

- Section 4.4: Undetermined Coefficients - Superposition Approach
- My lecture notes
- Handout: Gilles' handout on the Method of Undetermined Coefficients
- Handout: Graphs of Solutions and Annotated Version
- Handout: Beat Frequency Demo
- Video: Super-quick demos of beat frequency by SMU Physics: Demo with tuning fork (0:34 min) and Demo with oscilloscope app (0:53 min)

**Test 1 is tentatively scheduled for Wednesday of this week**.

#### Week 6: Feb 15 to Feb 19

- This week is Reading Week.

#### Week 7: Feb 22 to Feb 26

- Section 4.6: Variation of Parameters
- My lecture notes
- Handout: Explainer on Methodology
- Handout: Explainer on Why No +C in u's

- Section 4.7: Cauchy-Euler Equations
- My lecture notes
- Handout: Gilles' handout on the Constant coefficients and Cauchy-Euler equations
- Handout: Explainer on Cauchy-Euler equations
- Handout: Explainer on Quick Constant Coeffs vs. Cauchy-Euler

#### Week 8: March 1 to March 5

- Section 5.1: Linear Models: Initial-Value Problems
- My lecture notes
- Review: Gilles' handout on Linear combination of Sine and Cosine
- A student asked me what it would look like if you had damped oscillation plus an external force which is sinusoidal but with a slightly different frequency. As we've seen, damped oscillation looks like this. Undamped oscillation plus an external sinusoidal force can give a beat frequency. Damped oscillation with beats can look something like this (depends on the constants), but as you can see there is an initial "beat" state, which decays away until only the steady state solution (from the external force) is left.

**Test 2 covers the material up to this point**. Here is a brief review of the topics covered.

#### Week 9: March 8 to March 12

- Section 6.1: Review of Power Series
- Section 6.2: Solutions about Ordinary Points

**Test 2 is tentatively scheduled for this week or next: DX02 writes this Friday and DX01 writes the following Thursday**.

#### Week 10: March 15 to March 19

- Finish up 6.2.
- Section 7.1: Definition of the Laplace Transform
- My lecture notes
- Gilles' table of Laplace transforms
- Gilles' problem book on Laplace transforms

#### Week 11: March 22 to March 26

- Section 7.2: Inverse Transforms and Transforms of Derivatives
- My lecture notes
- Video: Finishing up Inverse Laplace example from last in-person lecture (6:44 min)
- Video: Laplace Transforms of Derivatives (7:52 min)
- Video: Solving IVPs using Laplace: Example 1 (4:14 min)
- Video: Solving IVPs using Laplace: Example 2 (10:26 min)
- Video: Solving IVPs using Laplace: Example 3 (10:31 min)
- Handout: MIT Math's Handout on the Heaviside Cover-up Mathod for Partial Fractions

- Section 7.3: Operational Properties I
- My lecture notes
- Video: Laplace transforms of translations on the s-axis (6:08 min)
- Video: Examples of Laplace transforms of translations on the s-axis (4:01 min)
- Video: Examples of inverse Laplace transforms of translations on the s-axis (6:08 min)
- Video: More examples of inverse Laplace transforms of translations on the s-axis (11:19 min)
- Video: Solving IVPs using Laplace and translations on s-axis: Example 1 (7:10 min)
- Video: Solving IVPs using Laplace and translations on s-axis: Example 2 (8:39 min)
- Sorry, I don't have any videos regarding translations on the t-axis (Heaviside function)

- Engineering link of the week: How to make a parabolic 8.4 metre mirror for the new Giant Magellan Telescope

**Test 3 covers the material up to this point**. Here are some review questions from the DX01 session on Thursday (DX02 didn't meet on Friday because it is a statutory holiday). Also, here are a few hints for WeBWorK Assign8.

#### Week 12: March 29 to April 2

- Section 7.4: Operational Properties II
- My lecture notes
- Video: Derivatives of Laplace transforms (10:03 min)
- Video: Solving IVPs using derivatives of Laplace transforms (7:15 min)
- We are omitting convolutions, and also transforms of periodic functions (useful for Electronics students).

- Section 7.5: The Dirac Delta Function
- Here is a hint for WeBWorK Assign9 Question 6.

#### Week 13: April 5 to April 9

- Section 8.1: Preliminary Theory - Linear Systems
- My lecture notes
- Video: Intro to systems of linear first-order DEs (7:27 min)
- Video: Verifying solutions to systems of linear first-order DEs (7:50 min)

- Section 8.2: Homogeneous Linear Systems
- My lecture notes
- Handout: Summary of solutions for homogeneous linear systems of DEs.
- Video: Homogeneous systems of linear first-order DEs - theory (8:36 min)
- Video: Homogeneous systems of linear first-order DEs - distinct eigenvalues, 2x2 example (11:15 min)
- Video: Homogeneous systems of linear first-order DEs - repeated eigenvalues, 3x3 example (8:32 min)
- Video: Homogeneous systems of linear first-order DEs - complex eigenvalues, theory (11:49 min)
- Video: Homogeneous systems of linear first-order DEs - complex eigenvalues, 2x2 example (8:24 min)

**Test 3 is tentatively scheduled for this week or next: DX01 writes this Tuesday and DX02 writes the following Tuesday**.

#### Week 14: April 12 to April 16

- Finish up 8.2.
- We will omit 8.3. If you'd like to see the lecture notes, please email me. I'm happy to go over them with you in office hours.