MATH 257 Study Guide - Midterm Guide: Medieval Commune, Taylor Series, Heat Equation
Document Summary
No calculators or electronic devices of any kind are permitted. There are 12 pages in this test including this cover page, blank pages, and the formula sheet. 1: [20 marks] for the ode initial value problem (1 + x)y + y = 0, y(0) = 2, y (0) = 3, Nd the rst 5 non-zero terms of the series solution about x = 0. 3: for the non-homogeneous heat equation problem ut = uxx + ex u(0, t) = 0, u(1, t) = 1. Use the notation uk n = u(xn, tk) to denote the values of u on the nite di erence mesh, and include how you propose to incorporate the bound- ary and initial conditions. In case it is useful, the taylor expansion formula is f (x + x) = f (x) + f (x) x + 1.
