# Math 137 – Spring 2016 – Assignments

You will find written assignments and projects, listed in order of due dates.  You can post questions and discussions about the assignments on the Piazza forum.

Problems are from the textbook: Hughes-Hallett, Calculus, Sixth Edition , Wiley, 2009.

Wednesday 1/27/2015 (before class): HW1: 1.2: #22; 1.4: #26; 1.5: #14, #16;  1.6: #31.  Mathematica problem: Reproduce this plot.  Your graph should be as shown, including the labeling, but I don’t care what color the graph is. Print out your graph, and staple it to the rest of your assignment.

Wednesday  2/3/2016 (before class): HW2: 12.3 #8, 10, 26, 28; 12.4 #12, 22. Mathematica problem:  Produce plots that explore the function f(x,t)=exp(-.15t)*exp(-(x-t)^2).
(1) Make a 3D plot, labeling the axes.
(2) Make a contour plot, labeling the axes.
(3) Make a plot that shows cross sections of the 3D graph for t=-1, 0, 1, 2. For this, put the x-axis horizontally. You will have to label each curve, so we know which one is which curve.
(4) This function represents a wave traveling along a canal with t time and x distance along the canal, is the wave traveling in the direction of increasing or decreasing x? How do your graphs convince you that you are correct?

Friday 1/5/2016 (before class) Project 1  Please form teams of 3 students. Each team will submit one report.  Here’s a rubric.

Wednesday  2/10/2016 (before class): 14.1 #18, 28, 30a; 14.2 #2, 14, 42, 46, 48. Mathematica problem:  Do Section 14.1 #34. Use complete sentences to answer the questions, and type in Mathematica. Produce a contour plot (using k=1) for the rest of the exercise, with axes labelled, and all 5 points of part (d) identified in some way.

Wednesday 2/17/2016 (before class) 14.3 #22, 30; 14.6 #18, 22; 14.7 # 30, 50.  There is no Mathematica problem this week.

Wednesday 2/24/2016 (before class) 10.1 #4, 10, 14, 18; 14.7 #32, 34.  Mathematica problem.  To create the degree n Taylor polynomial for f(x), centered at x=x0, in a form you can evaluate, you can use the command
g[x_] := Evaluate@Normal[Series[f[x], {x, x0, n}]]
Your assignment is to show the graph of the function $f(x) = e^{-0.3 x} \cos(2 x)$ together with a few of its Taylor polynomials. Use the window $0 < x < 10$, $-1.1 < y < 1.1$.  What degree is required to get visual accuracy in the range $0 < x< 10$ if you center at $x=0$?  If you center at $x = 5$

Wednesday 3/2/2016 (before class) 13.1 #10, 28, 32; 13.3 #4, 10, 24, 38, 52; 15.1#2, 8, 16,22; 14.4 #4, 34, 54, 66.  Mathematica problem.  By drawing contour plots, find FIVE critical points of the function
f[x_, y_] := Cos[ x – y] (1 – x^2 + 2 y ) Exp[ x y^2/(1 + x^2 y^2)]
in the window -3 < x < 3, -5 < y < 5.  Give at least one local maximum, one local minimum, and one saddle point. There are 11 critical points in the region to choose from.   Support each critical point with a convincing plot.  A convincing plot is a contour plot in a small region containing just the one critical point.  You can estimate the coordinates of your critical points from your plot.  Hint: you can add more contours using Contours -> n (where n is the number of contours that you want). With larger n you see more detail.  Note that a critical point lies at the intersection of the zero level contours of the two partial derivatives fx and fy.    You can show the zero level contour using Contours->{0}.

Wednesday 3/9/2016 (before class) 15.2 #18, 22, 28; 15.3 #20, 26, 32; Review exercises (p. 861) #36.

Wednesday 3/23/2016 (no assignment due.  Enjoy your spring break.)

Wednesday 3/30/2016 (before class) 5.1 #4, 5; 5.2 #8, 12, 32; 5.3 # 18, 19, 26; Chapter 5 Review Problems (p. 311) # 30; 6.2 #42, 66; 7.1 #14, 54; 7.2#8, 10.

Wednesday 4/6/1016 (before class) 7.6 #2; 8.1 #4; 8.2 #8; 8.4 #10; 8.7 #14, 16, 20; 8.8 #4, 8, 10;

Friday 4/15/2016 (before class) 7.5 #10; 7.6 #2, 6; 8.2#16; 16.1 #14; 16.2 #6, 44; 16.6 #4, 10.

Friday 4/15/2016 (before class) Capstone Reflection Paper: Please write reflections on two Capstone Talks you attend.  Write in googledocs, share the paper with me and post a public link on the course Moodle site. Any Math,Statistics, or Computer Science talks are ok.  Report on what the main point of the talk was:  what problem did it address? why is it of interest?  what did you learn? what was the best part for you?   Please feel free to comment on aspects of the presentation: what did you like? what would you do differently if you were giving the talk?

Wednesday 4/20/2016 (no assignment due this week)

Wednesday 4/27/2016 (before class, the final assignment) Work sheet on atmospheric temperature, 11.1 #2; 11.2 #18; 11.4 #24; 11.5 #14.  Use Mathematica to graph the solution to the DE $y'[x]=1-y[x]^2+x$ with initial value $y[0] = 1$. Please graph it on the window -2 < x < 2.