MATH 375T Uhlenbeck Computer Assignment 3 Due March 8 Use pplane and dfield to make plots to solve the following problems on page 200-201. When the problems says "sketch" you should make a computer plot. The programs dfield and pplane are directly available from the homepage of Professor John Polking at Rice University. To use them on the math department computers, go into mathlab and type either the single word dfield, or the single word pplane. Type your equation into the window that appears and click on the proceed button. Be sure that you size the window properly to show interesting behavior. If you quit the plot window, you will also quit dfield or pplane. Just leave it up. Problem 1(page 200) : a)-d). Use dfield to make plots of typical solutions to these equations. Problem 2(page 200): Problem 2 a)-d) Find the graphs either by hand or using the computer. Draw your direction fields (arrows) along the y axis of the graph (x=0). Problem 7(page 201): b) d) e) f) Use pplane to plot typical solutions to these linear systems of equations. Explain when zero looks stable. Problem 4: Experiment using pplane with the system of equations (for your choices choices of a > 0) dx/dt = 5x - 1.9axy - x^2 dy/dt = 5y - axy - y^2. Look for solutions in the first quadrant only for various choices of a> 0. What happens when a is small? What happens when a is largish ( say about 2) Play with values of a on the computer to get a rough estimate of the bifurcation point between the two behaviors you observe. Suggestion: Be sure you see the limit point when a = 0. This might involve changing the size of the window.