Important points for the Jan. 8 class

1. To clone the repository from a cocalc terminal:

   git clone https://github.com/phaustin/eosc213_students.git
   

2. Always rename your notebook to something unique (doesn’t matter what) before you start work. It you don’t, then the next item will bite you at some point.

3. At the start of a new assignment, or when we announce important repository changes/bugfixes, sync with our changes by doing the following:

   git fetch
   git reset --hard origin/master
   

   This will overwrite every file that you haven’t renamed, so make sure your work is safe before you do this!.

4. Don’t use the cocalc chat icon for questions – cocalc only has 4 employees, and we should give them a break if possible. Try us on piazza, and we will forward to cocalc if we don’t know the answer.

5. Workflow for this course:

   1. login to cocalc.com and sync to get the new assignment

   2. Work on your copy of the notebook using your cocalc account

   3. Download the ipynb file to your local machine when complete

   4. Upload that file to the appropriate canvas assignment

   5. We will grade and then comment on the assignment with a url you can go to see our corrections/remarks (if any).

Jan 10. Preparation

In preparation for the Thursday, January 10 lesson topic – An introduction to ordinary differential equations, please do the following (plan on taking 60 – 90 minutes):

• Watch the following Khan Academy Videos on youtube

  • Differential equation introduction: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-1/v/differential-equation-introduction

  • Writing a differential equation: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-1/v/writing-a-differential-equation

  • Do the multiple choice practice problems: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-1/e/write-differential-equations

  • Verifying solutions to differential equations: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-2/v/verifying-solutions-to-differential-equations

  • Practice problems: Verify solutions to differential equations: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-2/e/introduction-to-differential-equations-and-initial-value-problems

  • OPTIONAL: the two tutorials on slope fields. https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-3/v/creating-a-slope-field and https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-4/v/slope-field-to-visualize-solutions

  • Finding general solutions: https://www.khanacademy.org/math/ap-calculus-ab/ab-differential-equations-new/ab-7-6/v/separable-differential-equations-introduction

• BACKGROUND Reference: Section 4.1 Basics of Differential Equations from the openstax open-source textbook project: https://cnx.org/contents/HTmjSAcf@3.5:97_h7KFf@5/Basics-of-Differential-Equations Good examples and practice problems – which are excellent ways of engaging with the material and learning.

We will assume that you have reviewed the material before class. On Thursday, we will give you problems based upon this material that you will work out in class (a so-called flipped classroom), and review any material that you have not learned.

• To guide your study, the learning goals for this material are:

  • Recognize an ordinary differential equation (ODE).

  • Recognize that the solutions to ODEs are FUNCTIONS, not single numbers.

  • Be able to recognize the order of an ODE

  • Know how to read the various notations used to write ODEs.

  • Be able to distinguish between linear and nonlinear ODEs and why that is significant.

  • Be able to write a simple differential equation model of a system, given the description of the system.

  • Distinguish between general solutions and particular solutions.

  • Identify information required for a particular solution (boundary and initial conditions).

  • Distinguish between initial value problems and boundary value problems

  • Describe a few common methods of solutions (separable, and perhaps series based solutions).

  • Be able to confirm that a function “solves” the ODE.