Homework and Quiz Assignments and Due Dates

When handing in homework, put your name, course and section, which homework assignment, and date in the upper right corner of the 8.5x11 paper. Staple in the upper left corner. It should be clear from your paper what homework problems you are doing. You can put section 1.1 down and then do all the 1.1 problems. Please be neat.

Pet Peeve warning: Please do not hand in notebook paper with raggy edges.

Quizzes are given the day homework is due and are primarily over the homework due.

Suggested homework The math department has suggested homework selected from your textbook.

• Integration homework or quiz is due by the end of the day on July 7, 2011. It is worth 10 points. You will find what you need to do these integrals on the Integrals Worksheet (temporarily unavailable). Work these out and bring this sheet to class on the first day.
• Writing assignment 1 Please get this done by the end of the day on July 7, 2011. Take 10-15 minutes to introduce yourself and reflect on what a good teacher/good student is. Three points will be given for completing this assignment thoughtfully. This assignment is found in the discussion section on eLearning. You may give a peer review of your classmates responses, and comment on them.
• Notecard Assignment due Friday July 8, 2011, though I would appreciate it on Thursday if you have it done early. This assignment is worth 4 points. I would like to start getting to know you.
• Homework 1 due Monday, July 11, 2011 (8 points)
  Section 1.1: 22, 23, 25
  Section 1.2: 17, 18, 23
  Section 1.4: 5, 13 handed in; recommend doing 1-13 odd
  You should also practice with as much of the suggested homework as you need to master this material.
• MATLAB Assignment 1 due Tuesday, July 12, 2011 (13 points)
  • You will do problems 31-33 from section 1.1 of your textbook.
  • In addition to the questions from the textbook, you will also do/answer the following and hand in all relevant plots.
    • Choose an appropriate minimum and maximum values for the display window.
    • Plot the solution that goes through the (t,y) given for the problem: 31 (0,1), 32 (0,5), 33 (0, 2.5)
    • Use this solution to approximate y(5).
    • What does this solution do as t goes to +infinity?
    Put this information on the printout of your direction fields;this is what you will hand in. You can learn a lot about differential equations and direction fields by playing around with dfield8. Experiment!
• Homework 2 due Wednesday, July 13, 2011
  Section 2.1: 19, 22, 23
  NOTE on 2.1: you do not have to hand in the direction fields but you should understand how to get them with MATLAB, and what they show you
  Section 2.2: 19 (solve IVP only), 29, 30
  Section 2.4: 11, 25, 26
  Plus this question:
  If you have a linear equation y' + p(t)y = g(t), and p(t) and g(t) are continuous everywhere, can you have two solutions y1(t) and y2(t) so that for a< b y1(a) < y2(a) but y1(b) > y2(b)? Give an answer and explain your answer using complete sentences. Hint: Theorem 2.4.1.
  Remember: You should also practice with as much of the suggested homework as you need to master this material.
• 1st Day Handout homework is due by the end of the day on Friday July 15, 2011. It is worth 5 points. You will find all of the answers to this quiz on the finalized version of our 1st Day Handout (finalized). You only get one try at this assignment.
• Quiz 1 and Quiz 2 are now available. Both are due Sunday, July 17, 2011 at midnight. If you run into problems, please email me ASAP. Remember: I am much more forgiving for problems that I can deal with early than I am for last minute items.
• Homework 3 due Friday, July 15, 2011
  Section 2.3: 4, 12, 24
  Section 2.5: 15a, 20 NOTE: For 15a, you can use calculus techniques to figure out this plot. If you are feeling unsure and need help, use Matlab or Wolfram Alpha or a calculator to sketch the graph -- for these tools you may need to fix the constants r and K. You can then find the critical points, and determine the stability; the behavior of this is like a problem we discussed in class and that is in your book.
  Section 2.6: 21, 22 INSTRUCTIONS:
  • Show that the equation is not exact.
  • Show how to find the integrating factor as we learned in class.
  • Since the book gives you the integrating factor, check to make sure your work is correct.
  • Show that with the integrating factor multiplied in the equation is exact.
  • Find the solution.
  Section 2.6: challenge yourself by doing one problem from 25-29 (part a only). These integrals are sometimes very hard, so take your time, do a good job, and exercise your patience and your brain on the one you pick.
  Remember: You should also practice with as much of the suggested homework as you need to master this material.
• Quiz3 and Quiz4 are available on eLearning. They are due before the end of the day on Tuesday, July 19, 2011.
  Quiz 3 is over sections 2.3 (Modeling) and 2.6 (Exact Equations), it will take you longer than Quiz 4. Quiz 4 is over section 2.5 (Autonomous Equations).
  As before, you have 2 chances to take this quiz.
  If you have problems email me immediately. I am much more forgiving when I hear about problems early
  
• Homework 4 due Wednesday, July 20, 2011
  Section 3.1: 34
  Section 3.2: 17, 19
  Section 3.3: 14, 16, 20, 26
  Do the suggested homework for 3.4 and 3.6 before the exam on Friday! -- You do not need to hand this in.
  Remember: You should also practice with as much of the suggested homework as you need to master this material.
• A 10-15 minute Writing Assignment is up on eLearning and it is due at the end of the day on Wednesday July 20, 2011.
• Matlab Assignment 2 (10 points) due Thursday, July 21, 2011
  1. Use pplane8 to do Section 3.2: 12, 13.
     Print out your direction fields, put the other information requested in the instructions for the problem on them, and hand them in.
  2. By hand, find the equilibrium points (there are 2) of the predator-prey equations (also called the Lotka-Volterra equations) given by:
     dx/dt = 0.6x - 0.1xy
     dy/dt = -0.4y + 0.05xy
     Use pplane8 to plot the direction field near the equilibrium point with both x and y positive, and some solutions near this equilibrium point. Hand in your direction field with the work you did to find the equilibrium points by hand.
• A 10-15 minute Writing Assignment for after the exam will be available on eLearning at noon on Friday and it is due at the end of the day on Saturday July 23, 2011.
• Quiz 5 is up on eLearning due Monday July 25, 2011 at midnight. We will do it in class. You may use your outlines for section 4.1 and 4.2 to do this quiz, but not your book, the internet, etc. You have 15 minutes to complete it and 1 and only 1 try to get it right. Answers may be used more than once.
• Homework 5 due Thursday July 28, 2011
  Section 4.1: 13, 15
  Section 4.2:17, 20, 22
  Section 4.3:22, 26, 31 (suggest doing 30 too)
  Section 4.4 26, 36, 38
  Remember: You should also practice with as much of the suggested homework as you need to master this material.
• Quiz 6 will be available on eLearning from 10 am July 26 until midnight July 28, 2011. You only get one try on this quiz! It is over sections 4.1 to 4.4, primarily 4.3 and 4.4.
• Quiz 7 will be available on eLearning from 10 am July 27 until midnight July 29, 2011. It is existence/uniqueness and Cauchy-Euler Equations.
• Another writing assignment is posted on eLearning due midnight on Saturday, July 30, 2011. It asks about the method for solving the Cauchy-Euler equation and how things are going. It may take you 30 or more minutes to complete.
• Homework 6 due Monday August 1, 2011
  Sections 4.6 and 4.8 -- Do the suggested homework first (you do not have to hand this in).
  NOTE: We did not do variation of parameters with 1st order systems of equations. You can skip those problems
  The assigned problems are on eLearning.
  There are 3 parts to HW 6; in total they are worth 21 homework points.
  You have two tries for each part; you are expected to follow the guidelines for working together on homework and using outside resources in completing this assignment.
• Quiz 8 is on eLearning.
  It is due at midnight on August 1, 2011. You only get one try at this quiz. It is over section 4.6; the method of undetermined coefficients.
• Homework 7 due Wednesday, August 3, 2011
  Section 5.1: 18, 26
  Section 5.2: 20, 24; suggest also doing 25
  Section 5.3: 18, 20
  Section 5.4: 10, 12
  
• Quiz 9 and Quiz 10 are due Wednesday, August 3, 2011 at midnight. You have two attempts at each of these two quizzes. You may use your notes, and a Laplace table, except when instructed to find a Laplace transform by hand. These quizzes are over sections 5.1 - 5.3.
  
• MATLAB Assignment 3 (20 points) due Thursday, August 4, 2011
  MATLAB Instructions/Basics/Help
  
  1. You will use both of MATLABs ode45 and ode23s routines to solve
     y'' +4y' +(25/4)y = (37/4)cost + (5/4)sint
     with initial conditions
     y(0) = 2 and y'(0)= 2
     by turning it into a 1st order system, writing a function to represent the ODE, and plugging it in to each of the two ODE solvers.
  2. Use the method of undetermined coefficients to solve
     y'' +4y' +(25/4)y = (37/4)cost + (5/4)sint
     with initial condition
     y(0) = 2 and y'(0)= 2
     
  3. Now, you will plot your solution from ode23s, your solution from ode45 and your exact solution that you found by the method of undetermined coefficients on the interval t = 0 to 7*pi.
  4. If you see any differences in your three plots, attempt to explain why.
  5. What you hand in is
     1. the work you did to take the 2nd order DE into a 1st order system
     2. a copy of your function for the 1st order ODE system
     3. your 3 plots
     4. the work you did to get the actual solution via undetermined coefficients
     5. any explanation needed to explain the differences in the 3 plots.
  6. If you are clever in your use of MATLAB, I believe you can get all 3 plots in the same figure but not overlaid. I do not want to see overlaid plots.
  Some notes:
  • This assignment is harder than previous MATLAB assignments.
  • It is easy to make mistakes programming a function. I did. Start early, then you can get help if you need it. I called a friend in to my office to see what was up with my Matlab and after explaining what I was doing, I looked at my function file and immediately saw that I set x1' = x1 instead of = x2. But this was after a long struggle!
  • You will probably need MATLAB's elementwise multiplication or division operations in getting your actual solution. .* and ./ do multiplication and division elementwise; try this if you get "matrix dimensions do not agree" errors.
  • If you missed the day we did much of this in class, you will want to refer to my MATLAB Help file for instructions. A similar problem to this one is done as an example in that file.
• BEFORE the exam on August 5, you will want to do the suggested homework on all the sections from chapter 5 that the exam is over. I believe we will get to Section 5.7 but possibly not quite that far.
• Exam 2 is on Friday August 5, 2011 It is over sections 4.1-4.4, 4.6, 4.8, 5.1 - 5.5 up to the Unit Step Function. Periodic functions will not be covered on this exam. From section 5.5, I suggest doing as many problems from 1-20 as it takes to master the material. Note: Unit step functions are on the exam.
• MATLAB Assignment 4 (25 points) due Monday, August 8, 2011
  

  We are going to investigate the Lorenz Attractor using MATLAB.

  The Lorenz attractor is an example of a dynamical system. A dynamical system describes the position of a point in space (3-dimensional space in this example) over time. So it describes how a particle might move or how fluid might flow. The Lorenz attractor is derived from a simplified system to describe convection rolls in the atmosphere.

  The Lorenz attractor is governed by a system of 3 first order differential equations, with three constants in them. Given the values of the constants, and a starting value, the evolution of the Lorenz attractor is deterministic. You can calculate where the particle will go at every time.

  The Lorenz attractor is called an attractor because for given values of the three constants, the trajectories given by the equations after a long period of evolution are localized in a bounded region of space. I.e. the trajectories are attracted to one region of space.

  For certain values of the constants, the behavior of the Lorenz attractor is also chaotic. This means that if you start two particles from nearly identical initial conditions, after a long enough period of time, their trajectories will no longer be close together.

  The chaotic behavior of the Lorenz attractor makes it a strange attractor and a fractal. A fractal has self-similarity in a technical mathematical sense on all scales. The types of trajectories you see in the strange attractor are repeated over all time scales.

  Do a Google Search on the Lorenz Attractor. There is a good article on it on Wikipedia. You may not understand all of the article, but you can understand most of it.

  1. You will need to hand in a cover sheet with at least a one paragraph description of the Lorenz attractor and what you are doing in this assignment. I gave you some information above, and there is a lot more information available on the web. You need to include the equations to describe it an the values of the parameters you will use to get the strange attractor.
  2. In your cover sheet, write a second paragraph describing the butterfly effect, and tell whether or not you see it in your subsequent work on Matlab with the strange attractor. Hint: Google and Wikipedia are your friends, but don't feel the need to restrict yourselves to these. There are many other sources of information out there.
  3. Identify the system of first order differential equations that governs the attractor. These need to be included on your cover sheet. You are going to program these equations into MATLAB.
  4. Identify the values of the three constants which give the strange attractor. This information also goes in your cover sheet.
  5. Using ode45 in MATLAB with initial conditions at or close to (1, -1, 1), find two trajectories that start from nearly the same point, and, if you can print in color or in a black/white/greyscale way, use plot3 to show that you get two very different trajectories from the two very close but not the same starting values.
  6. Help for plot3 is available in MATLAB (type help plot3), and there are some instructions here:
     MATLAB Instructions/Basics/Help
  7. Using ode45 and ode15s in MATLAB with initial conditions (1, -1, 1), over a time scale from 0 to 100 show that you get two trajectories that start from same point but that give very different trajectories. If you can print in color or in a black/white/greyscale way, use plot3 to show that you get two very different trajectories from the two ODE solvers with the same starting values. (I believe ode45 gives the better plot here.) You will want to use the command
     t = linspace(0, 100, 10000);
     to get your time values; you can plug t directly into ode45 or ode15s
  8. You will also hand in a copy of the function you use with ode45 and ode15s to model the dynamical system.
  9. While you've got the plot on your computer, rotate the plot you get from ode45 around. Can you see how the Lorenz attractor actually does look like a butterfly?
• Quiz 11 and Quiz 12 are due Tuesday, August 9, 2011 at midnight. You have two attempts at each of these two quizzes. You may use your notes, and a Laplace table. Quiz 11 is over periodic functions and the delta function. Quiz 12 is optional and over convolution (in your book, not covered in class); it will replace your lowest quiz grade if you do it.

(C) 2011 Jean Marie Linhart, all rights reserved.