l. Derive (5b). (6b), and (6c). 2. Verify the calculations in Example I of the text. Find out experimentally how many new you need to obtain the solution of the linear system with an accuracy of 35. 3. Use of symmetry. Conclude from the boundary values in Example I that an = on and 1422 = on. Show that this leads to a system of two equations and solve it. 4. Floor grid of 3 x 3 inner points. Solve Example 1. choosing h = 1} = 3 (instead of h = 153 = 4) and the some starting values. 510 GAUSS ELIMINATION, GAUSS-SEIDEL lTERATION 2 J' 1 In. 0 1 2 3 3 Fig. 456. Problems 5-10 ID For the grid in Fig. 456 compute the potential at the four internal points by Gauss and by 5 Gauss-Seidel steps with starting values 100. 100. 100, 100 (showing the details of your work) if the boundary values on the edges are: 5. u(l, U) = 60. u(2, 0) = 300.1: = 100 on the other three edges. 6. tr = 0 on the left, x3 on the lower edge. 27 93:2 on the right, x3 - 272: on the upper edge. 7. Lb on the upper and lower edges, Uu on the left and right. Sketch the equipotential lines. 8. u = 220 on the upper and lower edges. [10 on the left and right. 9. u = sin it\" on the upper edge. 0 on the other edges, 10 steps. in. u = x'on the 1oweredge,81 54y2 + y'enutetight, x4 - so:2 + 31 on the upper edge. y\" on the left. Verify the exact solution 3'4 Maya + y\" and determine the error