Author Archives: Jonas Reitz

OpenLab #4: Study Guide

Hi everyone,

This post contains the instructions for the Study Guide project.  Our goal is to create a study guide that will be useful both for the students in this class, and for future students.  This project will require an investment of time & energy on your part, and will be given a corresponding weight in your OpenLab grade (equivalent to two OpenLab assignments).

NOTE: your Study Guide should NOT be a comment in reply to this post, but instead should be a new Post that you create (see the “Resources” section below for help on this).  Creating a post means that you can save your work, and come back and edit it later.  You also have much more control over things like formatting, inserting images and videos, and so on.

Instructions.

  1. To get started, create a new post (HINT: click the “plus” sign in the grey bar at the top of the screen).
  2. Give your post a title that makes sense
  3. Select the Category “Study Guide” (from the box on the right side)
  4. Add at least 3 tags (you choose) (from the box on the right side, below “Categories”)
  5. Your post should include
    1. Overview.  Explain what the topic is about.
    2. Sample problem.  Give a sample problem, and explain how to solve it.
    3. Videos or images.  Please include at least 3 videos or images in your post that you personally found helpful.  Be sure to include a brief description.
  6. 500 words minimum (no maximum – write as much as is needed).
  7. Don’t forget to click either “Save Draft” or “Publish” from the topmost box on the right side.  “Publish” will make your post public on the main page of the site (but you can still edit it later), “Save Draft” will save your work without making it public.

Question: What if more than one person has the same topic?

  • Option 1: you can work together on a single post (this is preferred – but you will each be responsible for writing at least 500 words)
  • Option 2: you can work independently (you each create your own post)

Question: When is it due?

  • For topics covered BEFORE Spring Break (through Section 3.7), your Study Guide is due April 30th.
  • For topics covered AFTER Spring Break, your Study Guide is due May 18th (beginning of Finals Week).

Question: I saved a draft, how can I find it so I can work on it some more?

  • Saved drafts of posts can be accessed through the Dashboard:
    • Make sure you are logged into the OpenLab
    • To access the Dashboard, click the link “MAT 2680 Differential Equations” in the gray bar at the very top of the screen
    • Select “Posts” from the menu on the left side of the screen, and scroll through to find your post.  If you wish, you can show only posts that are “Drafts” by clicking the appropriate link near the top of the page (below the main title “Posts”)

Resources that may help you:

  • How to create a new post.
  • How to insert a video or image – look at the help topics here.
  • How to use mathematical notation on the OpenLab (like \int \frac{e^t}{t^2} dt).  This is done using the (very common in professional circles) mathematical markup language LaTeX — if you ever publish professionally in math or most sciences, you will end up learning this!  Luckily, it’s not too hard to get started — take a look at this assignment from a past Calculus class, which includes an introduction to writing LaTeX on the OpenLab.

Extra Credit

For extra credit, comment on another student’s Study Guide post. Your comment must say something substantive (more than just “great post!” or “very helpful” or “I don’t understand”) – tell us why you feel that way, or add something to the post that you think is missing, or (politely) point out an error if you think you see one, or suggest another video or other resource etc.  You can earn up to 3  extra credit points by commenting on multiple posts.

 

Study Guide Topic Assignments

If you do NOT appear on this list, please contact me immediately!

Study Guide Topic Username
2.1 Linear Equations; Method of Integrating Factors rahmanhasan718
2.1 Linear Equations; Method of Integrating Factors rmorel91
2.2 Separable Equations dhiraj
2.2 Separable Equations jiwei
2.2 Separable Equations (Homogeneous) diallo11368
2.2 Separable Equations (Homogeneous) ricardoferro
2.4 Bernouli Equations mrknowit22
2.4 Bernouli Equations wenyuli
2.4 Difference between Linear and Nonlinear Equations (Existence and Uniqueness) attareb212
2.6 Exact Equations vliang88
2.6 Exact Equations kmendez1994
2.7 Numerical Approximations: Euler’s Method samsonx711
2.7 Numerical Approximations: Euler’s Method dsantos
3.1 Homogeneous Equations with Constant Coefficients (second order linear) mattiie
3.1 Homogeneous Equations with Constant Coefficients (second order linear) jdelgado
3.1 Homogeneous Equations with Constant Coefficients (second order linear) enriquebron6
3.3 Complex Roots (of the Characteristic Equation) chand
3.3 Complex Roots (of the Characteristic Equation) rex19941
3.3 Complex Roots (of the Characteristic Equation) ltsakuxsasu648
3.4 Repeated Roots steven328
3.4 Repeated Roots hxie
3.4 Repeated Roots carolinam926
3.5 Non-homogeneous Equations; Method of Undetermined Coefficients pak1s0ul
3.5 Non-homogeneous Equations; Method of Undetermined Coefficients chowdhuryshawn
3.5 Non-homogeneous Equations; Method of Undetermined Coefficients rana
3.7 Electrical Circuits skane17
3.7 Electrical Circuits anzamul hyder
5.2 Series Solutions Near an Ordinary Point kumar
5.2 Series Solutions Near an Ordinary Point jramroop4
6.1 Definition of the Laplace Transform christianpinto
6.1 Definition of the Laplace Transform abraham
6.2 Laplace Transform: Solution of the Initial Value Problems (Inverse Transform) vanessa2793
6.2 Laplace Transform: Solution of the Initial Value Problems (Inverse Transform) aayush
8.1 The Euler or Tangent Line Method medinalex13
8.2 Improvements on the Euler Method danielmwong
8.2 Improvements on the Euler Method 520crystal

 

Grading: 10 points total (equiv. to 2 OpenLab assignments)

  1. Basics (one point each, 4 total):
    1. Title that makes sense
    2. Category “Study Guide”
    3. At least 3 on-topic tags
    4. 500 words minimum
  2. Content (two points each, 6 total):
    1. Overview
    2. Sample problem/solution
    3. Three videos/images with brief description

Midsemester Grades are posted

Hi everyone,

I’ve finished grading Exam #2, and I incorporated your scores into the Midsemester Grade.  You can find your Midsemester Grade on the Grades page (click the link in the menu above) – if you forget the password for the Grades page, send me an email or ask a fellow student.  The Midsemester Grade contains detailed scores for all the WeBWorK and OpenLab assignments to date, plus the first two exams – you can find your Exam #2 grade in the Midsemester Grade breakdown.

Let me know if you have any questions,
Prof. Reitz

 

WeBWorK #11b: Overdamped, Underdamped, and Critically Damped

Hi everyone,

As you work through the assignment on Circuits, you will come across questions about damping, and you may notice that we never spoke about this in class.  Figuring out whether a circuit is over-, under- or critically damped is straightforward, and depends on the discriminant of the characteristic equation — the discriminant is the part under the radical sign when you use the quadratic formula (it controls the number and type of solutions to the quadratic equation):

The Discriminant = b^2-4ac

  • Under-damped: Discriminant < 0  (the characteristic equation has two complex roots)
  • Critically Damped: Discriminant = 0 (the characteristic equation has a repeated root)
  • Over-damped: Discriminant > 0 (the characteristic equation has two distinct real roots)

But that’s cheating!  What does damping actually mean?

Great question!  We will not discuss damping in detail in this class, but if you work with electrical circuits this is a concept you will run into often.  Take a look here for a basic overview:  http://en.wikipedia.org/wiki/Damping

Hope your Spring Break is going well,
Prof. Reitz

 

 

WeBWorK #9 UPDATE

Hi everyone,

Just a quick update – a few students had reported issues with some of the later problems in WeBWorK #9 (e.g. that the system would not accept a correct answer).  These problems have been resolved, and the problems should work correctly now – go ahead and try them again.  Carefully doublecheck the question to make sure the numbers have not changed before you proceed.

As a reminder, this assignment is due on Tuesday, 4/14.

Have a wonderful Spring Break,
Prof. Reitz

WeBWorK madness! — Assignment #9 extended to April 14th

Hi everyone,

I know you are all working very hard on the WeBWorK assignment #9.  As you have probably discovered:

  1. the problems can be quite long (especially the last couple!)
  2. a few students have run into WeBWorK bugs that incorrectly mark correct answers as “wrong” (I am working to resolve these currently, and hope to have them worked out in the next few days)

Because of this, I have extended this assignment until after Spring Break – it is now due (along with WeBWorK #11b) at the end of the day on Tuesday, April 14th.  Your focus right now should be preparing for the exam on Thursday – good luck!

Prof. Reitz

OpenLab #3: Flipping the class – Taylor Series

Hi everyone,

After Spring Break we will be launching into a new and incredibly useful topic – using Taylor Series to solve differential equations.  Of course, using this method requires you to remember something about Taylor Series (uh oh!).  You should have studied them in Calculus, probably Calculus II or III.  Don’t remember? This is your chance to refresh your memory.

Assignment (Due Tuesday, April 14th, BEFORE CLASS):  Watch all of the following videos carefully.  As you are watching, make a note of any questions you have.  When you are done, complete the following exercise:

Exercise:  Find at least the first 10 terms of the Taylor Series for y=e^{2x} at the point x=0.

Finally, post a comment here confirming that you watched the videos, and including the following:

  1. Confirm that you watched the videos (say something like “I watched all the videos.”)
  2. Post ONE of the terms you found while solving the exercise above (for example, you might say “One of the terms is \frac{4x^5}{15}“).  CHALLENGE: Don’t use the same term as anyone else.
  3. Ask a question about Taylor Series, either about one of the videos (tell me which one), or about Taylor Series in general.  If you don’t have a question, tell me something about Taylor Series – what do you like about them, what don’t you like, what’s the big deal, etc…

Here are the videos:

Video 1: Taylor/Maclauren Series intuition

 

Video 2: Taylor Series for Cosine at x=0 (Maclaurin Series)

Video 3 (OPTIONAL): Taylor Series for Sine at x=0  (NOTE: This video is OPTIONAL, but it might help you better understand the next video)

Video 4: Visualizing Taylor Series Approximation

Undetermined Coefficients: What happens when everything cancels?

An excellent question that I received in email today with regards to WeBWorK #9:

Hi professor Reitz, on problem number two for the new homework, when I try to solve for the particular solution, everything on the left side cancels.

This will happen when the expression on the right side of the equation also happens to be one of the solutions to the homogeneous equation.  We deal with it in much the same way we dealt with repeated roots in homogeneous equations: When guessing the particular solution to the nonhomogeneous equation, multiply your guess by t (for example, use y=Cte^{t} instead of y=Ce^{t}.  Here’s an example.

Example: y''-7y'+10y = 10e^{2t}

The general solution to the associated homogeneous equation y''-7y'+10y=0 is:

General solution: y=Ae^{2t}+Be^{5t}

Notice that one of the basic solutions involves e^{2t}, which matches the right hand side of the original equation.  Because of this, we would make the following guess for a particular solution:

Guess: y=Cte^{2t}

Notice that when you take the derivative, you will still end up with a term involving just Ce^{2t} (without the extra “t”), which will allow the left hand side of the equation to equal the 10e^{2t} on the right side.

Let me know if you have any questions (post a comment!),
Prof. Reitz

WeBWorK extension

WeBWorK assignments #6, 7, 8, formerly due tonight, have been extended by two days.  They are now due this Thursday, 3/26, at midnight.

Regards,
Prof. Reitz

Exam 2 Review is posted

UPDATE: I added one problem (#5) to the Exam Review, from the topic exact equations —  you may remember that we covered this in class just before the first exam, but it was not on the first exam.

Hi everyone,

The review sheet for Exam #2 (which will take place on Thursday, April 2nd) is posted on the Handouts page.  Let me know if you have any questions.

Best regards,
Prof. Reitz

WeBWorK 6: What are these “basic solutions” in part c) of the questions??

Hi everyone,

Just a quick note about part c) in problems like these:

Screen Shot 2015-03-20 at 1.12.05 AM

 

The “basic solutions” refer to the two solutions that come from plugging the roots of the characteristic equation into our “best guess” formula y=e^{rt}.

For example, if the two roots are r=3, r=-5, then the basic solutions would be:

e^{3t}, e^{-5t}

Let me know if you have any followup questions  (or questions about anything else in the current WeBWorK assignment).

Regards,
Prof. Reitz