- Download Maple session 8/27 (Right-click. Save as...)
- PDF version of Maple session 8/27
- Lecture 8/27
- Video 8/27
- S 1.2 Initial-Value Problems 8/29
- Draining the tank 8/29
- Video 8/29
- S 1.3 Models 9/3
- Download Maple session 9/3
- View PDF of Maple 9/3
- Video 9/3
- S 2.1 Direction Fields 9/5
- Download Maple session 9/5
- Video 9/5
- Download Maple 9/10
- Separable Equations 9/10
- Video 9/10
- Linear ODEs 9/12
- Video 9/12
- Exact Differential Equations 9/17
- Download Maple 9/17
- Video 9/17
- S 2.4 #8 9/19
- Download Maple for S 2.4 #8 9/19
- Substitution Rule 9/19
- Video 9/19
- Download Excel Spreadsheet for Euler's Method 9/24
- Euler's Method 9/24
- Video 9/24
- Nonlinear Equations 9/26
- Download Maple for 9/26
- Some 3.2 Solutions 10/1
- Draining the Tank 10/1
- Linear ODEs 10/3
- Quick 'n' Dirty Linear Algebra Stuff 10/3
- Maple Stuff for Linear Algebra 10/3
- View Maple in PDF
- Maple built in class 10/3
- View PDF of Maple 10/3
- Video 10/3
- 4.2 Notes 10/8
- 4.2 and 4.4 Notes 10/8
- Building some Characteristic Polynomials in Maple
- Miscellaneous Maple 10/8
- 4.4 Maple 10/8
- 4.4 Notes 10/8
- Video from 10/8 Kind of all over the map, from Chapter 3 Written Work to 4.2 Theory, and a lightning-
fast intro to 4.3 and 4.4. But I think you'll see, when you start working it, that you already knew a lot of this stuff, and it's pretty natural.
Good material for the Midterm.
- Notes (Edited. Better.) 10/10. I fixed my answer to
Ajay's question about Chapter 3 Written work. The water-skier question. My trig substitution was OK, but
I forgot the integral of the sine, and I went blind about the arctanh term.
- Video from 10/10
- Cramer's Rule Notes for 4.6 (Background)
- Cramer's Rule Video.
- 4.6 Variation of Parameters Notes 10/17
- 4.6 Variation of Parameters Video 10/17
- 4.6 #6 10/17
- 4.6 Homework Notes 10/17
- 4.7 Lecture Notes for 4.7 and 4.8 10/22
- 4.7 Cauchy-Euler Equations Theory Video 10/22
- 4.8 Green's Function Theory
- Maple Document for 4.7 #6 10/22
- Maple Doc in PDF for 4.7 #6 10/22
- Live talk from 10/22 - There's some "new" theory regarding
3rd-order equations and 3x3 matrices.
- Section 4.8 #1 and Some Theory for 10/24
- Notes to Accompany the 4.8 #1 Video 10/24
- Maple (Download) for 4.8 #7 from the questions Right-
click the link to download.
- Notes for 4.8 #6
- 4.10 #1 Video 10/29
- 4.10 #2 Video 10/29
- 4.10 #6 Video 10/29 Notice how the initial
conditions are incorporated into the solution. When we get y', we can plug in y'(1) = 2 to
clean up the constants.
- 4.8 #9 - I got caught flat-footed with the BVP.
It's not that difficult or that much different. But it IS different, so I will be uploading
a better set of notes and video for this exercise.
- 4.8 #9 Live Video (sucks) 10/29 - The one, below, is some better.
- How We're re-organizing the content, a bit Video 10/29 - I recorded
the wrong screen, but all that was on screen was the WebAssign page for our class, which you can look at
while I speak. Sorry about that, but yeah: Skip 4.9, Chapter 5 (for now) and jump to 6.1 after we do 4.10.
- 4.8 #9 Video 10/29 - Not real happy with its quality, but
better than the one, above! Bottom line is to be
good at variation of parameters. Notice it didn't ask you to write the Green's Function? I built one, and worked
the exercise using Green's Function. You just have to evaluate the two integrals, separately, to obtain anything
by hand. This exercise
is pretty easy if you use your normal bag of tricks and don't try to shoe-horn a Green's Function in, to no purpose.
- 10/31 Maple for Section 6.1 - A few commands and palette moves for power series and
partial sums in Maple.
- 10/31 PDF transcript of the Maple - for viewing convenience without Maple.
- 10/31 6.1 #6 Notes
- 10/31 6.1 #6 Video - A very elegant and all-purpose way to obtain practical,
working solutions, accurate to whatever precision desired, especially if you have a CAS like Maple to do your heavy lifting.
Worth noting is that Maple wasn't used for this particular exercise.
- 10/31 Video Intro to 6.1. Mainly discussing the homework
and #4 in some detail. Also some Maple demos.
- 10/31 Notes to Accompany Video for 6.1 #4
- 10/31 Live Lecture Notes - Just a small question about Chapter 4 Written Work #1. Speaking
of which, let's make that assignment due Sunday night or Monday. The 6.1 should probably be done by end of day Tuesday,
after you've had time to ask me some questions on it. Thence to 6.2 and 6.3.
- Brief discussion about how things are set up and that 1st Chapter 4 Written question.
- 11/5 - Right-Click to download Maple for 6.2 #7
- 11/5 - View PDF of Maple for 6.2
- 11/5 6.2 Video. Ordinary and Singular Points and Radius of Convergence
- 11/5 6.2 #7 - Initial conditions make it easier!
- 11/5 6.2 #2 Video
- 11/5 6.2 #2 Notes
- 11/5 6.2 #2 Maple Download
- 11/5 6.2 #2 PDF of Maple for #2
- 11/7 Notes from Class - Some bloviating about Chapter 7. We're on course to
finish up Chapter 6 by early next week. I'm prepping for 6.3 as we speak.
- 11/7 - 6.3 Notes - Power Series Solutions about Singular Points. This is where all the
notes are going, for all the lectures in 6.3
- 11/7 - 6.3 Video Intro - Power Series Solutions about Singular Points
Look for more installments on 6.3 in the next day or two.
- 11/8 - 6.3 Video Intro Part II
- 11/8 - 6.3 #1
- 11/8 - 6.3 Intro Notes (updated) - Be sure to hit refresh, because you likely
have loaded an earlier version of this file, above
Coming up: Maple's "series" command. We're not done with 6.3, yet.
- 11/8 - Right-Click to Download Maple for 6.3
- 11/8 - View PDF of Maple for 6.3
That should wrap up 6.3, except for a video on #8, which I sneakily added late, just to torture people. I cheated
you of a deep discussion of Cases i, ii, and iii, but I think you have sufficient info to go on for the exercises
given. If I hadn't added #8, I don't think we would've needed to deal with those 3 cases in Section 6.3.
- 11/12 - Notes for 7.1 - Intro to Laplace Transforms
- 11/12 - Video Intro to 7.1 - Intro to Laplace Transforms
- 11/12 - Right-Click to Download Maple for 7.1
- 11/12 - Maple for 7.1 Doc in PDF format
As of 11/12, it looks like people are finishing up their Chapter 6 Written Work. Deadline: Wednesday, November 13th, 11:59 pm.
It was suggested that we delve
into the applications in Chapter 5. That's probably a good idea. Maybe not the only good idea. What do you think we should
cover after Section 7.3?
- 11/14 - Section 7.2 Intro Notes
- 11/14 - Section 7.2 Video - Featuring "convert(F(s),parfrac,s)" command.
- 11/14 - 7.2 Maple Download (Right-Click)
- 11/14 - 7.2 Maple for viewing (PDF)
- 11/19 - 7.1 - 7.3 Cheat sheet
- 11/19 - 7.3 Notes (Draft)
- 11/19 - Right-click to download Maple document for 7.3
- 11/19 - PDF version of 7.3 Maple for easy viewing
- 11/19 - 7.3 Video #1 - Covers The First Translation Theorem
and Examples 1 and 2
- 11/19 - Live Video - Apparently it didn't record.
- Where we are (7.3) and where we're going (7.4, 7.5, plus as much of Chapter 5 as we can handle).
- Scolding Connor and Gavin for distracting me. If you just turned off your video, I wouldn't notice that
I'm not being noticed. 30 years of in-class lecture is hard to totally overcome, but in an asynchronous format,
all I'm really concerned with is that you're learning, I'm helping, and that I'm not wasting your time. I think there's
a lot of time waste in live lecture settings, especially for me, with one foot in old habits and one foot in new ways.
I think I forgot how to do live talks or lost the knack when I went full-on remote. So many hours preparing on-demand
content gets in the way of the live experience, and I'm sorry for that.
- 11/19 - 7.3 Video #2 - Example 3, in which we apply Laplace Transforms
to a 2nd-order ODE. Note that this may also be solved by Method of Undetermined Coefficients, which goes
quite a bit quicker than Laplace Transforms. I spend the last minute or two of the talk discussing how this method
is actually very efficient (to program), compared to some other methods, especially for "batches" of equations,
where you just have to program the thing, once, and solve multiple equations.
- 11/19 - 7.3 Video #3 - Second Translation Theorem and examples
- 11/19 - 7.3 Video #4 - Finishing off the examples
- 11/21 - 7.4 Notes (Draft) -
- 11/21 - Right-Click to download Maple for 7.4
- 11/21 - PDF of Maple for 7.4
- 11/21 - 7.4 Intro Video Theorem on Laplace Transform of
t f(t) is -d/ds(F(s)) and Example 2
- 11/21 - 7.4 Convolution Video
- 11/21 - 7.4 Transform of an Integral Video
- 11/21 - 7.4 - Example 7 - Volterra Integral Equation Video
- 11/21 - 7.4 Integro-Differential Equations
and Example 8 Video
- 11/23 - 7.4 Transforms of Periodic Functions Video
- Theorem 7.4.3
- 11/26 - Example 9 - Transform of a Square Wave Video
- 11/26 - Example 10 - Solve an LR-Circuit Video
- 11/26 - 7.5 - Dirac Delta Function Notes
- 11/26 - 7.5 - Dirac Delta Function Video -
Definition and Theorem 7.5.1 regarding its Laplace Transform Video
- 11/26 - Example 1 Video - We solve a differential equation with Dirac impulse function as driving force.
- 11/27 - Chapter 7 Written Work #9 Maple Download
- 11/27 - Chapter 7 Written Work #9 Maple PDF
- 11/27 - Notes for Chapter 7 Written Work #9 - I miscopied the darn
thing, but you can see my approach to the system, which we didn't cover in Section 7.6. I was just going to take it
out of the Written Work, but I think you should be exposed to this sort of thing before leaving this course.
Note - This isn't the most elegant Maple implementation. I don't want the most elegant code. I want
the method that mirrors what we do by hand the best (shooting for higher-level thinking with lower-level code).
- 12/02 - Chapter 7 Written Work #10 with Maple
- 12/02 - PDF of Maple for #10
- 12/02 - Right-Click to Download Maple for #10
- 12/03 - Notes
- 12/03 - Video. Actually gave something of a live talk. - This recording is
quite a bit better than the live lecture. I cut out most of the floundering around and sped up some of the writing.
- 12/10 - Video for the Final - I run through pretty much what's on it.
- 12/10 - Notes for the Final
Call me at 970-290-0550 to make an appointment. I have 2 of you lined up
and 2 of you who need to schedule the written final. Deadline is Friday.