1 / 12

Section 10.2.2 Euler's Method

Section 10.2.2 Euler's Method. Diff. Equ. February 24, 2009 Berkley High School. Consider a Differential Equation: y'=x+y. We would like an approximation of the curve of y(x) that goes through y(0)=2. What is the slope at y(0)=2? slope is 0+2=2

scarlett-mckay
Download Presentation

Section 10.2.2 Euler's Method

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 10.2.2Euler's Method Diff. Equ. February 24, 2009 Berkley High School

  2. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(0)=2. • What is the slope at y(0)=2? • slope is 0+2=2 • Let ∆x = 1. What is our best guess as to the value of y(1)? • 2+2=4. We think that a point on that curve is approximately y(1)=4

  3. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(1)=4. • What is the slope at y(1)=4? • slope is 1+4=5 • Let ∆x = 1. What is our best guess as to the value of y(2)? • 4+5=9. We think that a point on that curve is approximately y(2)=9

  4. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(2)=9. • What is the slope at y(2)=9? • slope is 2+9=11 • Let ∆x = 1. What is our best guess as to the value of y(3)? • 9+11=20. We think that a point on that curve is approximately y(3)=20

  5. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(0)=2. • What is the slope at y(0)=2? • slope is 0+2=2 • Let ∆x = .5. What is our best guess as to the value of y(.5)? • 2+.5*2=3. We think that a point on that curve is approximately y(.5)=3

  6. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(.5)=3. • What is the slope at y(.5)=3? • slope is .5+3=3.5 • Let ∆x = .5. What is our best guess as to the value of y(1)? • 3+.5*3.5=4.75. We think that a point on that curve is approximately y(1)=4.75

  7. Consider a Differential Equation: y'=x+y • We would like an approximation of the curve of y(x) that goes through y(1)=4.75. • What is the slope at y(1)=4.75? • slope is 1+4.75=5.75 • Let ∆x = .5. What is our best guess as to the value of y(1.5)? • 4.75+.5*5.75=7.625. We think that a point on that curve is approximately y(1.5)=7.625

  8. Exercises • Section 10.2: 19-24 all

More Related