Category: Assignment Instructions (Page 2 of 5)

Due Monday, October 17

Step 1

Choose one of the questions from Test #1 that you did not receive full credit for and re-solve the problem. Submit your complete solution (a photo of your written work or typed using LaTeX) as an OpenLab post with title Test #1 Solutions and the type of equation you are solving and with category Test #1 Solutions.

There were different versions of the test with similar questions. Make sure you don’t choose a problem whose solution a classmate has already posted.

Step 2

Read your classmates’ solutions and find one for another question on your version of Test #1. Submit a comment on their post describing how you approached that question similarly or differently or any questions or suggestions you have.

Due Wednesday, October 12

Numerical methods provide us a way to approximate solutions of initial value problems without actually having to solve them. In Chapter 3, we see three of these methods for initial value problems of the form $y’=f(x,y)$, $y(x_0)=y_0$:

• Euler’s method
• Improved Euler’s method
• Runge-Kutta method

For Part 1 of Project 2, you will create your own calculator to approximate the solution of one initial value problem using all four of these methods, each with different step sizes. You will not perform your calculations by hand; instead you should use spreadsheet software like Excel or Google Sheets. You may write your own computer program instead of using a spreadsheet if you prefer.

Here is an example of the type of spreadsheet you will create (though this spreadsheet does not conform to all the instructions below).

\begin{math} \frac{x^6 y^8 z}{x ^2y^5} \end{math}