Euler's equation of numerical solution.

Description
Initial value problem is analysed. Euler's equation of numerical solution is defined and derived. A curve is convex if its second order derivative is positive.Similarly a curve is concave if its second order derivative is negative. How differential equation can be used to get solutions without actually calculating the solutions, is explained here. The methods of finding numerical errors are discussed.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 2: Euler's Numerical Method for y'=f(x,y): Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed November 2, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc