APPM 2360 Midterm: appm2360spring2014exam2_sol
Document Summary
On the front of your bluebook write: (1) your name, (2) your student id number, (3) recitation section (4) your instructor"s name, and (5) a grading table. Text books, class notes, and calculators are not permitted. Problem 1: (35 points) let the matrix a and column vector ~b be given by: 1 2 (d) (e) (f) (at ) 1 = (a 1)t = . Problem 2: (30 points) consider the following system of ode"s: In answering the following questions, ensure that the graph is large enough to be read easily. In the x-y plane: (a) find and plot all equilibrium points. (b) find and plot the vertical nullclines. Indicate the direction of the vector eld on the vertical nullclines. (c) find and plot the horizontal nullclines. Indicate the direction of the vector eld on the horizontal nullclines. (d) state the stability of all equilibrium points. (e) plot the solution with initial condition (x0, y0) = (1, 1).
