In this lesson, students are introduced to Euler's method, a basic numerical method for solving differential equations. The method involves finding the slope of the line element at the starting point, choosing a step size, and continuing the solution until reaching the next point. The lesson includes an example of using Euler's method to solve a non-trivial differential equation, and also discusses the limitations of the method and how to determine if the solution curve is convex or concave.
Euler's Numerical Method for y'=f(x,y) and its Generalizations -- Lecture 2. How to find numerical solutions to differential equations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
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