A very long telephone transmission line is initially at a constant potential u0. If the line is grounded at x 0 and insulated at the distant right end, then the potential u(x, t) at a point x along the line at time t is determined from 02 u 0x 2 2 RC 0u 0t 2 RGu 0, x . 0, t . 0 u(0, t) 0, lim xSq 0u 0x 0, t 0 u(x, 0) u0 , x 0, where R, C, and G are constants known as resistance, capacitance, and conductance, respectively. Solve for u(x, t). [Hint: See in Exercises 15.1.]

CalculusandAnalyticGeometryI SPRINGSEMESTER2016 INSTRUCTOR:DR.M.O’LEARY 25 January 2016 1.1: A Preview of Calculus We will be solving two problems: ● the tangent line problem (How do you find the slope of a curve) ● and the area problem (How do you find the area under a curve) 1.2: Finding Limits Graphically and Numerically Let f(x) = 2x + 1. What value if any...