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# Euler's Method

This prezi is about the development and history of Euler's Method and an explanation as to how to use it in everyday calculus...

by

Tweet## Kaitie Walker

on 16 May 2011#### Transcript of Euler's Method

The History and Explanation of the Euler's Method... What is Euler's Method??? Euler's Method is a numberical approach to approximating the particular solution of differential equation y'=F(x, y) that passes through the point (x ,y ). 0 0 The Mastermind Behind the Euler's Method... Leonhard Euler created Euler's method. Euler was born in Bâle on April 15, 1707, and died at St. Petersburg on September 7, 1783. Euler was the first of six children and his father was a Lutheran minister. Leonhard was married twice. He earned his masters degree at age 16 at the University of Basel and contributed alot to modern day calculus. Euler's Written Works... Introductio in Analysin Infinitorum- 1748

Institutiones Calculi Differentialis- 1755

Institutiones Calculi Integralis- 1770

Anleitung zur Algebra - 1770

Theoria Motuum Planetarum et Cometarum- 1744

Theoria Motus Lunaris- 1753 In Plain English... Basically Euler's Method is a way to find the approximate area under the curve of a function. Putting the Method into Action... Example 1 y'=x-y Passes through the point (0,2) and use a jump of h=.5 y = y +hF(x , y )= 1+(.5)(0-2)=1

y = y +hF(x , y )=1+(.5)(.5-0)=1.25

y = y +hF(x , y )=1.25+(.5)(1-1.25)=1.125

y = y +hF(x , y )=1.125+(.5)(1.5-1.125)=1.3125

y = y +hF(x , y )=1.3125+(.5)(2-1.3125)=1.65625 1 0 0 0 2 1 1 1 3 2 2 2 4 3 3 3 Your "h" value is the jump

The "x" and "y" values are the point that the equation is passing through Example 2 y'=2x+y y = y +hF(x , y )=1+(.2)(2*0+1)=1.2

y = y +hF(x , y )=1.2+(.2)(2*.2+1.2)=1.52

y = y +hF(x , y )=1.52+(.2)(2*.4+1.52)=1.984

y = y +hF(x , y )=1.984+(.2)(2*.6+1.984)=1.263

y = y +hF(x , y )=1.263+(.8)(2*.8+1.263)=.723

y = y +hF(x , y )=.723+(.2)(2*1+.723)=.395 1 0 0 0 Passing through the point (0,1) and use a jump of .2 5 4 4 4 2 1 1 1 2 2 3 2 3 3 3 4 4 4 4 5 5 5 6 5 For Further Help: Quiz Time!!! 1. What is the Euler's Method used for?

2. How many children were in Euler's family?

3. How old was Euler when he got his masters degree?

4. Use Euler's Method to solve this equation...

d'=x+2y passing through the point (0,3) with a jump of .5

5. Use Euler's Method to solve this equation...

d'=x+y passing through the point (0,4) with a jump of .5 Solutions!!! 1. To find the approximate area of an equation under the curve.

2. 6 children

3. 16 years old

4. 206.25

5. 123.145 Sources... http://www.maths.tcd.ie/pub/HistMath/People/Euler/RouseBall/RB_Euler.html

http://www.math.wichita.edu/history/men/euler.html

http://www.mathsisgoodforyou.com/people/euler.htm

Full transcriptInstitutiones Calculi Differentialis- 1755

Institutiones Calculi Integralis- 1770

Anleitung zur Algebra - 1770

Theoria Motuum Planetarum et Cometarum- 1744

Theoria Motus Lunaris- 1753 In Plain English... Basically Euler's Method is a way to find the approximate area under the curve of a function. Putting the Method into Action... Example 1 y'=x-y Passes through the point (0,2) and use a jump of h=.5 y = y +hF(x , y )= 1+(.5)(0-2)=1

y = y +hF(x , y )=1+(.5)(.5-0)=1.25

y = y +hF(x , y )=1.25+(.5)(1-1.25)=1.125

y = y +hF(x , y )=1.125+(.5)(1.5-1.125)=1.3125

y = y +hF(x , y )=1.3125+(.5)(2-1.3125)=1.65625 1 0 0 0 2 1 1 1 3 2 2 2 4 3 3 3 Your "h" value is the jump

The "x" and "y" values are the point that the equation is passing through Example 2 y'=2x+y y = y +hF(x , y )=1+(.2)(2*0+1)=1.2

y = y +hF(x , y )=1.2+(.2)(2*.2+1.2)=1.52

y = y +hF(x , y )=1.52+(.2)(2*.4+1.52)=1.984

y = y +hF(x , y )=1.984+(.2)(2*.6+1.984)=1.263

y = y +hF(x , y )=1.263+(.8)(2*.8+1.263)=.723

y = y +hF(x , y )=.723+(.2)(2*1+.723)=.395 1 0 0 0 Passing through the point (0,1) and use a jump of .2 5 4 4 4 2 1 1 1 2 2 3 2 3 3 3 4 4 4 4 5 5 5 6 5 For Further Help: Quiz Time!!! 1. What is the Euler's Method used for?

2. How many children were in Euler's family?

3. How old was Euler when he got his masters degree?

4. Use Euler's Method to solve this equation...

d'=x+2y passing through the point (0,3) with a jump of .5

5. Use Euler's Method to solve this equation...

d'=x+y passing through the point (0,4) with a jump of .5 Solutions!!! 1. To find the approximate area of an equation under the curve.

2. 6 children

3. 16 years old

4. 206.25

5. 123.145 Sources... http://www.maths.tcd.ie/pub/HistMath/People/Euler/RouseBall/RB_Euler.html

http://www.math.wichita.edu/history/men/euler.html

http://www.mathsisgoodforyou.com/people/euler.htm