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Euler's Method and Contributions by Leonhard Euler

Explore Euler’s Method, a way to solve differential equations approximately, pioneered by the blind mathematician, Leonhard Euler. Learn the base of natural logs, pi, and summation, and practice applying Euler’s Method with various increments.

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Euler's Method and Contributions by Leonhard Euler

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  1. 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

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

  3. We will practice with an easy one that can be solved. Initial value: There are many differential equations that can not be solved. We can still find an approximate solution.

  4. Exact Solution:

  5. 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.

  6. Euler’s Method Use Euler’s Method with increments of ∆x = .1 to approximate the value of y when x = 1.3 and y = 3 when x = 1.

  7. Euler’s Method Use Euler’s Method with increments of ∆x = .1 to approximate the value of y when x = 1.3 and y = 3 when x = 1.

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