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Euler’s Method

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Euler’s Method

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  1. Euler’s Method

  2. Euler’s Method Leonhard Euler made a huge number of contributions to mathematics, almost half after he was totally blind. (When this portrait was made he had already lost most of the sight in his right eye.) Leonhard Euler 1707 - 1783 Greg Kelly, Hanford High School, Richland, Washington

  3. (function notation) (base of natural log) (pi) (summation) (finite change) It was Euler who originated the following notations: Leonhard Euler 1707 - 1783

  4. There are many differential equations that can not be solved. We can still find an approximate solution. Euler’s Method is used to approximate values on the solution graph to a differential equation when you can’t find the specific solution. Remember that a function and its tangent have nearly equal values near the point of tangency. The is called linearization. Euler’s Method just uses this concept repeatedly.

  5. Euler’s Method: Euler’s Method is simply linking together several tangent lines until you reach the new point.

  6. Use Euler’s Method to approximate y(2) using increments of given the initial value (1,2).

  7. Exact Solution:

  8. This is called Euler’s Method. It is more accurate if a smaller value is used for dx. It gets less accurate as you move away from the initial value.

  9. Homework Page 423 #1,2,4,9,10,11,12 Page 416 #1-4