A coaxial cable is made of a 0.1-in.-square inner conductor and a 0.5-in.-square outer conductor. The potential at a point in the cross section of the cable is described by Laplace's equation. Suppose the inner conductor is kept at 0 volts and the outer conductor is kept at 110 volts. Find the potential between the two conductors by placing a grid with horizontal mesh spacing /? = 0.1 in. and vertical mesh spacing /: = 0.1 in. on the region D = {(x, y) | 0 < x, y < 0.5 ). Approximate the solution to Laplace's equation at each grid point and use the two sets of boundary conditions to derive a linear system to be solved by the Gauss-Seidel method.

L5 - 6 There is a base that occurs frequently in applications and is especially useful in calculus. It is the irrational number e. NOTE: e ≈ The importance of e: Consider the slope of the tangent line to the graph of x f(x)= b at the point (0,1). If b =2 f b =3 If b =2 , m tan ≈ 0.69 and if b =3 , m tan ≈ 1.1. We will see the slope of the tangent lin ye= toe at x =0 is exactly 1.