MATH 172 -- Mathematical Modeling for the Life Sciences

Professor Matt Miller
miller@math.sc.edu

Section 1 MWF 11:15-12:05 in LeConte 105
Text: Principles and Practice of MathematicsCOMAP, Springer, NY, first edition, 1997


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  • Class topics and problems
  • Jan. 14-18. Modeling and difference equations. See if you can get a copy of your MATH 122 or 141 final exam from your previous instructor, and see if you can still do the problems. Knowing how to do the hand calculations is vital for this course, but we will also use these problems and your solutions to give you some idea what the calculator/computer can (and should) do, and what it can not (or should not) do. Read 1.1, read 1.2 and do problems 1acd, 2acd, 10, 11, 12, read 1.3 and do problems 1ab, 2ab, 5, and read section 1.4. Comparison with the continuous case, constrained and unconstrained growth models.
  • Jan. 23-25. Sequences and differences Do problems 1, 3, 5, 6 from 1.4; problems 1, 4, 10, 13, 15 from 1.5; and problem 1 (all parts) from 1.6. Read the text through 1.6 and the handout on calculators and sequences.
  • Jan. 28-Feb. 1. Solving difference equations, series Read section 1.9 and do problems 1def, 2, 5, 8, 9. Read section 1.10 up to "Finding zeros" on page 87, and do the Chapter 1 review problems 1ab, 2b, 5ad, 10ad, 12 on page 94.
  • Feb. 4-8. Sequence plotting, vectors and polar coordinates Be sure you know how to do sequence graphing on your caclulator. Finish up sections 1.9, 1.10, and the review as indicated above. Go on to read sections 2.1 and 2.2, and do problems 1, 2, 14 from 2.1, and 2, 8, 12, and 14 from 2.2.
  • Feb. 11-15. Continuous logistic model, sequences (cont.), polar coordinates, exam Finish up the problems from 2.1, do the problems from the logistic model handout, and do the polar coordinate problems listed above.
  • Feb. 18-22. Trig functions, matrices Read the handout from the Math 122 text on periodic functions; do problems 1, 5-8, 11, 13, 26 from section 1.12 in the handout, and problems 1, 2, 3, 7, 8, 9, 12, 15, 16 from section 4.5 in the handout.
  • Feb. 25-Mar. 1. Vectors and matrices Read pages 121-126 in the text and do problems 4 and 7 on page 126. Also find a column vector u so that Au = (5/2)u, where A is the matrix with top row [1 1] and bottom row [3 1/2]. Read about geometric transformations, and do problems 17a and b on page 185. Read section 3.7.
  • Mar. 4-8. Transformations and Leslie matrices Work through the Maple worksheets Transformations.mws , Leslie2.mws , and also eigen.mws if you like. Do problems 1, 2, 3, 4, 7 from text section 3.7.
  • March 11-15. Spring Break Have fun (and think about your projects a little).
  • March 18-22. Age (stage) structured models, exam #2 Continue working on your projects and on the problems from 3.7
  • March 25-29. Introduction to probability: counting principles Do problems 1-5, 7-11 in section 4.1, problems 1, 3, 5, 8, 10 in 4.2, and 7-9, 28 in the end of chapter review, page 298.
  • April 3-5. Permutations and combinations, combining multiplication and addition principles, Do problems 1-6, 11, 13, 16, 10, 12, 14 from 4.3, and 7-9, 18, 33, 35 from the chapter 4 review.
  • April 8-12. Counting problems (cont.), probability Do problems 3, 5, 7, 8ab (also a', b' as given in class) from 8.1, and problems 1-4, 6-10, 12, 13 from 8.2. Do problems 1, 4-8, 12, 13 from section 8.3.
  • April 15-19.
  • April 22-26.
  • April 29-May 1.

  • Exams and Projects
  • Friday, Feb. 15: FIRST EXAM: continous and discrete unconstrained (exponential) growth, continous (logistic) model for density dependent (constrained) growth, net growth vs. per capita growth rates, difference equations with constant higher order differences and polynomial solutions, linear homogenous and non-homogeneous first order difference equations, equilibria, stability, long term behavior of solutions, how to use tables, proportionality, writing model equations from verbal descriptions, and geometric series. Study the 2 quizzes and sections 1.1-1.6, 1.9 in the text.
  • FIRST PROJECT (topics assigned in class, due Monday, 23 March)
  • Friday, March 22: SECOND EXAM (vector operations, including dot product, polar coordinates, trig functions: amplitude, period, derivatives, matrices and transformations, weather models, eigenvalues and eigenvectors, age-structured population projection models)
  • Monday, April 22: THIRD EXAM (chapter 4 and parts of 8)
  • SECOND PROJECT (topics distributed in class, due Monday, April 29)
  • FINAL EXAM: Saturday, May 4 (2-5 pm) in LC 113

    • Last modified: May 1, 2002