Category Archives: OpenLab Assignment

OpenLab #4: Study Guide

Posted on April 14, 2015 by | 7 comments

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

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OpenLab #3: Flipping the class – Taylor Series

Posted on March 30, 2015 by | 50 comments

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

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OpenLab #1: Advice from the Past

Posted on February 10, 2015 by | 67 comments

Last Spring I taught this same course for the first time.   At the end of the semester, I gave my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2680, to give advice to entering students. Write at least three sentences … describing what you would tell them.

To see the assignment and the students’ responses, follow this link.

Your assignment, due on Thursday 2/19 at the start of class, is to:

  1. Read through ALL the responses (there are 53 of them – many are quite short).
  2. Write a reply to this post (150 words minimum, not including quotations) responding to all of the following:
    1. What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    2. Based on this advice, what changes can you make right now to help you with this course?

Extra Credit. For extra credit, write a response to one of your classmates’ comments.  Do you have any advice?  Be kind.

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