Lab1_Section2_4

Lab1_Section2_4 - Math 306 Lab 1 Eulers Method Printed Name...

This preview shows pages 1–2. Sign up to view the full content.

Math 306 – Lab 1 Euler’s Method Printed Name: Please carefully work all of the following problem(s). You must SHOW YOUR WORK to receive ANY credit! This lab will investigate Euler’s Method for approximating the solutions to differential equations. As an example, the simple differential equation dy dx = e - x 2 y (0) = 1 . has a unique solution – namely y ( x ) = R x 0 e - u 2 du . Unfortunately, there is no elementary way to perform this integration. Instead, we shall try to approximate the solution. Consider the general IVP dy dx = f ( x, y ) , y ( x 1 ) = y 1 . The idea is We pick an initial point, say ( x 1 , y 1 ) The slope through the point ( x 1 , y 1 ) is given by f ( x 1 , y 1 ). We move a small distance along the slope segment through this point to the next point ( x 2 , y 2 ). At the point ( x 2 , y 2 ), we have a new slope given by f ( x 2 , y 2 ). We now move a small distance along the slope segment through ( x 2 , y 2 ) to the next point ( x 3 , y 3 ). Etc. A more mathematical version of this process is: Choose a step size, say h > 0.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern