MATH 210 Midterm: MATH 210 2012 Winter Test 2
Document Summary
Instructions: do all fteen questions in part a, each worth 2 points, do all four questions in part b, each worth 5 points, total 50 marks, justify all answers, write your answers in booklets. Part a: do all fteen questions, each worth 2 marks. [2] calculate the jacobian matrix of the system f1(x1, x2) = sin(x1x2) f2(x1, x2) = ex1x2 x2. [2] consider the scalar, autonomous de below du dt. = u2 u3 with u(0) = 2. Approximate u(0. 2) using two steps of euler"s method with time step k = 0. 1. It is not necessary to simplify your answer. [2] consider the function f (x) = 1 3x + x3 which is known to have a root x [0, 1]. Beginning with this interval, do two steps of the bisection method. [2] bob is writing a matlab code that is supposed to implement newton"s method f (x) = cos(x) x2. to nd a root of.
