Math 426 Mathematical Modeling in Biology Homework
Fall 2009
- Papers are always due at the beginning of class.
- Use pencil and eraser rather than ink. Messy papers will not be graded.
- Fold your paper along the long axis, and on the outside write
- Your full name
- Math 426
- HW #
- Box #
- HW 17 due Tuesday, November 24, at the beginning of class
- Consider the logistic model with Allee Effect, that is x' = rx(x-a)(1-x/K), where a,r,K > 0. List all of the equilibria, and find the eigenvalue at each equilibrium. From the eigenvalue, determine the stability of the equilibrium.
- Find the phase line portrait (PLP) for x' = -2(x-3)(x+3)^4
- Draw the bifurcation diagram for the logistic model with Allee effect using "a" as a bifurcation parameter. Allow "a" to take on all real values. At what values of "a" do bifurcations occur, and what type of bifurcations are they?
- HW 16 due Tuesday, November 10, at the beginning of class
- HW 15 due Tuesday, November 3, at the beginning of class
- HW 14 due Thursday, October 22, at the beginning of class
- HW 13 due Tuesday, October 20, at the beginning of class
- Read Ch. 5.
- p. 78: 3 [Typos: (??) should be (g). In part (r), b /= mua should be b > mua.]
- Get ready for your Midterm by making sure you have all your programs running, etc.
- HW 12 due Thursday, October 8, at the beginning of class
- HW 11 due Tuesday, October 6, at the beginning of class
- Work through all of the problems in Appendix A. Check your answers. Do not hand this in.
- p. 50: 1, 4, 6, 7(a-i)
- HW 10 due Thursday, October 1, at the beginning of class
- p. 60: 3-4 [Please reduce the graph images so you can put several on one page. Also, note that EFchaos seems to require that you use 2.718^(-c*x) rather than exp(-c*x). Crazy, I know! Finally, for 4d, you can scale the y-axis inside the bifurcation diagram diaglog box by checking "manual sclaing".]
- Read Ch 3. Bring any questions to class.
- HW 9 due Tuesday, September 29, at the beginning of class
- p. 35: 20 [This is not a typical homework problem; it is a short scientific project. You will need to type up your work into a short paper. Your paper should include a title page along with an Introduction, Methods, Results, and Discussion, and it will include tables & captions, and figures & captions. Take very seriously the instruction to "present your work in a complete, precise, and organized fashion". I will be instructing the grader to grade accordingly.]
- Read Ch 4.
- p. 60: 1, 2
- HW 8 due Tuesday, September 22, at the beginning of class
- p. 34: 17-19 [Hint: for the program in #19 you should attach your input files and your output. Also, you can use the MatLab syntax >>mean(len) to compute the average, or "mean", of the vector len. Your programs will be fairly short, and they will not involve fminsearch; you are not estimating parameters. You will use the parameter estimates from Table (2.9).]
- HW 7 due Thursday, September 17, at the beginning of class
- Work assigned problems on the board.
- HW 6 due Tuesday, September 15, at the beginning of class
- p. 33: 6, 10, 14. [Note: #6,10 are calculus problems--get out the old calc book! Remember that "show" means "prove" in math-speak.]
- Type a one-paragraph proposal for your class project. Be as specific as possible. Hand this in separately.
- HW 5 due Thursday, September 10, at the beginning of class
- Write and run the three programs. For each one, hand in hard copies of (1) the input file; (2) the programs; and (3) the screen output and graph. Staple each of the three sets. Clip the three sets together with a paper clip. Each student must write and run the programs for his or her self. It is ok to ask each other for help.
- Play with the programs and commands in MatLab (or Octave). Make sure you understand what each line of the program is doing.
- HW 4 due Tuesday, September 8, at the beginning of class
- Read Ch. 2. Mark any questions you have and bring them to class.
- p. 34: 9, 11, 12, 13 [Hint: For number 13, use fminsearch.]
- HW 3 due Thursday, September 3, at the beginning of class
- Print out Ch. 2.
- If you have had Calculus III (double integrals), do p. 18, #10. If you have not had Calculus III, do p. 18, #12. In the latter problem, you are finding the inflection points of the function f given in (1.4), that is, you are finding the values of x that make d^2f/dx^2=0.
- p. 19: 18-20, 23
- HW 2 due Tuesday, September 1, at the beginning of class
- Reply to the 5 questions from the article (use separate piece of paper; put your name on it). Turn the questions and answers in together (stapled).
- Read Ch. 1. Mark anything you don't understand and ask about it in class.
- Do Ch. 1: 1-4, 6, 8, 9 (put this on a separate piece of paper).
- If you have a laptop, bring it to class on Tuesday with Octave (or MatLab) loaded and ready to use.
- HW 1 due Thursday, August 27, at the beginning of class
- Download Octave and the Octave manual to the computer you will be using for class.
- Print out Ch. 1 of your textbook (double sided would be nice in order to make your book thinner), and place it in a dedicated notebook.
- Read the handout article. Write down 5 questions you have about the contents of the article, and turn this in for your homework. Your peers will be evaluating these, so do a good job.
