Class Links- Weeks 1 to 7
- Review Material - Read these at your leisure.
- Week 1: August 24-28. Introduction and 2.1
- Monday, Aug 24 (Introduction, 1.3-1.4)
- Wed, Aug 26. Section 1.1 and some review (integration by parts)
- Friday, Aug 28: Section 2.1 (Linear, first order DEs)
- Week 2: Aug 31 - Sep 4
- Monday, Aug 31- Section 2.2 (Separable DEs with Homogeneous DEs in the HW)
- Group Quiz 1 is out this week. See the instructions and groups on Canvas. Solutions due on Friday.
- Video: One last exercise from Section 2.1
- Video: Section 2.2 (Separable DEs) and an extra homework solution.
- Video: Homogeneous DEs (from the homework section in 2.2, and on the quiz)
- Video REVIEW: Integrate via Partial Fractions (Part 1 of 2)
- Video REVIEW: Partial Fractions- How to find the constants (Part 2 of 2)
- Homework: 1, 3*, 5*, 7, 9*, 11, 16, 20, 31, 35. NOTE: This is the corrected homework to turn in. You can use
technology (for example, the online plotter) to help you determine appropriate intervals. Only turn in solutions to 3, 5, and 9. These will be due on Thursday, Sep 3.
- Wednesday, Sep 2: Section 2.3 Modeling
- Video 1: Introduction to Modeling
- Video 2: Tank Mixing
- Video 3: Money
- Video 4: Parachutes!
- Homework: 3, 4*, 5, 9, 10*, 12, 13, 16, 23, 28*.
For these problems, Maple or Mathematica or Wolfram Alpha may be used (or something equivalent). Due Tues, Sep 8 (With Friday's HW).
- Friday, Sep 4: Section 2.4 - The question of existence and uniqueness.
- Video 1: The theory
- Video 2: Examples
- Video 3: More examples
- Video 4: Bernoulli Equations (From the homework section in 2.4)
- Homework: 1, 3, 4*, 7, 9, 13*, 15, 21, 22(a,b)*, 28*, 32*. Due Tues, Sep 8 (With Sep 2nd HW).
- Week 3:
- Monday, Sep 7: Section 2.5 (Autonomous DEs)
- Video 1: Section 2.5, Autonomous DEs, Part 1
- Video 2: Autonomous DEs, Part 2
- Video 3: Autonomous DEs, Part 3
- Video 4: Autonomous DEs, Part 4
- Homework: Section 2.5, 1-7 odd, 8, 10, 11, 14, 15, 22-24, 25, 26. NOTE: I won't be collecting homework
from you later this week as I would not be able to return it before the exam. Please try all the problems however!
- Wednesday, Sep 9: No new material.
- Friday, Sep 11: Section 2.6 (Exact Equations)
- Video 1: Section 2.6, Exact Equations, Part 1 of 4
- Video 2: Section 2.6, Exact Equations, Part 2 of 4
- Video 3: Section 2.6, Exact Equations, Part 3 of 4
- Video 4: Section 2.6, Exact Equations, Part 4 of 4
- Homework: 1, 3, 4, 10, 13, 15, 17, 18, 19, 22.
- Week 4:
- Monday, Sep 14: No new material. Study for exam.
- Wed, Sep 16: Exam available on Tuesday, Wednesday.
- Fri, Sep 18: Section 3.1- Second order DEs.
- Quick NOTE: If we were in class, I would go through the material in the first three videos and perhaps the next one or two videos in one class period, then finish up the other videos in the next. I've included all three of the "linear operator" videos
here so you can decide if you have time today or save them for next time.
- Video 1: Section 3.1 (Part 1 of 3)
- Video 2: Section 3.1 (Part 2 of 3)
- Video 3: Section 3.1 (Part 3 of 3)
- Video: Linear Operators (Part 1 of 3)
- Video: Linear Operators (Part 2 of 3)
- Video: Linear Operators (Part 3 of 3)
- Homework on Cramer's Rule and Linear Operators
- Homework: Sect 3.1: 1, 3, 10*, 13, 15, 17, 18*, 19, 22, 24* and handout (Try all, turn in 4(a,c)* and 5(e)*). Homework due on Tuesday, Sep 22.
- Week 5
- Monday, Sep 21: 3.2- Theory behind second order equations.
- Video 1: Review and the Wronskian.
- Video 2: Finding all solutions; The fundamental set
- Video 3: Abel's Theorem
- Video 4: Finish Abel's Theorem and its significance.
- Video 5: Summary and Exercises
- Video 6: More exercises
- Homework: Sect 3.2: 1, 2, 4, 7, 9, 14*, 16, 18*, 28, 29*, 35. Homework due on Thursday, Sep 24.
- Wed, Sep 23: Complex numbers, some useful trig and Section 3.3 (Complex roots to the characteristic equation).
- Fri, Sep 25: Finish second order linear homogeneous equations, look at Reduction of Order.
- Section 3.4 (Video 1 of 2)
- Summary of Section 3.4, examples (Video 2 of 2)
- Homework: Section 3.4: 1, 3, 5, 6, 8, 12*, 14, 16, 18*, 24*, 25, 34, 38. Due Tuesday, Sep 29.
- Week 6:
- Mon, Sep 28- Section 3.5 The Method of Undetermined Coefficients.
- Slides from the lecture, no pauses, PDF format
- Video 1: Method of Undetermined Coefficients.
- Video 2 - Finish the method, do lots of examples
- Homework: Section 3.5: 1, 3, 5, 7*, 13, 15, 19(a), 20(a)*, 21(a), 22(a)*, 23(a). Homework due on Wednesday (before you start your break!)
- Wed, Sep 30: Nothing new - Catch up day!
- Fri, Oct 02: October Break
- Week 7 (Mid-semester)
- Mon, Oct 5: Section 3.6 and Complexification.
- Wed, Oct 7: Section 3.7: The Mass-Spring Model
- Fri, Oct 9: Section 3.8: Analysis of the Mass-Spring Model. See the notes and homework write up below that replaces 3.8 in the book.
- Optional videos from YouTube about Beating and Resonance (some were seen in the slides from Friday).