6.2.6-Numerical Integration: Gauss Quadrature Part 1 скачать в хорошем качестве

6.2.6-Numerical Integration: Gauss Quadrature Part 1

These videos were created to accompany a university course, Numerical Methods for Engineers, taught Spring 2013. The text used in the course was "Numerical Methods for Engineers, 6th ed." by Steven Chapra and Raymond Canale. In the equations for the unknown coefficients. I forgot to multiply by the width, (b-a). The picture is right, but the equations are given below. The integral on the left: c0*f(a) + c1*f(b) = 1*(b-a); f(x) = 1, so c0*1 + c1*1 = b-a c0 + c1 = b-a The integral on the right: c0*f(a) + c1*f(b) = 0*(b-a); f(x) = x -c0*(b-a)/2 + c1*(b-a)/2 = 0 Solving these gives c0 = c1 = (b-a)/2. To get the solution, it is easiest if we do equation 2 first. -c0*(b-a)/2 + c1*(b-a)/2 = 0 Divide both sides by (b-a)/2 (which will never be 0). This gives -c0 + c1 = 0. Thus, c0 = c1. Substituting this into equation 1 gives c0 + c0 = b-a 2c0 = b-a c0 = (b-a)/2.