Mathematical Modeling (MATH 420/620)

Fall 2015 course website

Lectures: 4:00pm-5:15pm, Mon & Wed, 24 Aug - 7 Dec, 2015 in DMS 106 (map)    
Final: 2:45-4:45pm on Monday, 14 Dec 2015. (PDF of Fall 2015 Final Week Schedule).
Syllabus: Click here to download (PDF). (Updated 24 Aug 2015)

Office Hours: M 11am-12, W 1-2pm, F 10-11am (or by appointment) in 220 DMSC

Website for Required Textbook:
WebCampus will be used for this course:

Software Resources

R: Install R, then RStudio. Also, see my R page.
Google's Style Guide for R scripts:
R Intro for Math 420 (PDF)

Maxima:A free alternative to Maple for symbolic computations. Download Maxima or the slightly more user friendly version (preferred) wxMaxima.
Maxima Resources: Instant Maxima (PDF) by Steve Ellner. Also, see Richard H. Rand's Introduction to Maxima, or see the Maxima website.

LaTeX Editor: Use TeXStudio if you don't have a preferred editor.
Getting Started with LaTeX: You might find my LaTeX Resources page useful.
Writing Equations in LaTeX: The AMS Short Math Guide for LaTeX (PDF) is excellent!
Homework Template: Want to turn in homework that looks like this PDF? Download this zip file and open the TeX document in TeXStudio.

Tentative Schedule

Week Monday Wednesday Homework & Notes
1: Aug 21, 23 Syllabus;
Introduction & overview
Methodological approach to math modeling
Slides: Week1-W.pdf
Download Ch 9 (PDF) from Ellner and Guckenheimer (2006), available at
Read Up to 9.2.1 well, skim 9.2 - 9.6, Read 9.7-9.8
Read up to 1.2 in the text.
2: 8/31, 9/2 Textbook Ch. 1
Intro to R
Slides: Week2-M.pdf
Optimization (Ch 1; Ch 2)
Intro to R programming
Install R, then RStudio.
Homework: Go through Section 2 in the R Intro for Math 420 (PDF), work the exercises of your choice. Email an R script of those solutions to the instructor, with file name LASTNAME-HW1.R. Due: 9/9. Please try to follow Google's R Style Guide!
Optional: The exercises in Ch1-Ex-1.1.R
3: Sep 7,9 NO CLASS (Labor Day) Optimization (cont'd)
Intro to Maxima (PDF)
Discuss Project
Slides: Week3-W.pdf
Homework: Due Monday -- Status update on projects. Topic? Any journals you plan to look through?

Due Wednesday (9/16) -- Hw2 (PDF). LaTeX file to use as a template for typed solutions (OPTIONAL!): hw2.tex
SOLUTIONS: hw2-solns.pdf, hw2-solns.R, hw2-solns.wxmx
4: Sep 14, 16 Optimization (Cont'd)
Slides: Week4-M.pdf
Optimization (Cont'd)
Slides: Week4-W.pdf
Homework: Due Wednesday (9/23) -- Hw3 (PDF; corrected 9/21). LaTeX file: hw3.tex
SOLUTIONS: hw3-solns.pdf, hw3-solns.R
5: Sep 21, 23 Dynamic Models, Ch.4
Slides: Week5-M.pdf
Dynamic Models, Ch.4
Slides: Week5-W.pdf
Homework: Due Wednesday (9/30) -- Hw4 (PDF).
LaTeX file: hw4.tex
SOLUTIONS: hw4-solns.pdf, hw4-solns.R
6: Sep 28, 30 Analyzing Dynamic Models, Ch.4-5
Slides: Week6-M.pdf
Analyzing Dynamic Models, Ch.4-5
Slides: Week6-W.pdf
Homework: Due Wednesday (10/7) -- Hw5 (PDF).
Solutions: hw5-solns.pdf, hw5-soln1-bonus.wxmx, hw5-lorenz.wxmx
7: Oct 5, 7 Equilibrium Stability Analysis Numerical Solutions to ODEs (Ch 6) Example equilibrium Stability analysis for the tree competition example (4.1) in wxMaxima: stability-analysis-example.wxmx. See also Instant Maxima (PDF).
Optional Reading: Dushoff et al (1998)
R code (for Weds): numerical-solutions-ODEs.R
Updated version: numerical-solutions-ODEs-v2.R
8: Oct 12, 14 Numerical Solutions to ODEs (Ch 6) & Bifurcation Diagrams
HW. DUE WEDS 8/14: bifurcation-diagram-HW.R
HW #6: Due 8/14: Finish modifying this R script from class Monday to create a bifurcation diagram for the given predator-prey model.
Solution: bifurcation-diagram-HW-solns.R
9: Oct 19, 21 Intro to Probability Models (Ch 7) Intro: Probability Distributions (no HW)
10: Oct 26, 28 Probability Distributions
Poisson Processes,
Useful functions in R
HW #7: Due Wed (11/4) -- HW7 (PDF). LaTeX file: hw7.tex
Solutions: hw7-solns.pdf
11: Nov 2, 4 Poisson Processes
Slides: Week11-M.pdf
Markov Chains
Slides: Week11-W.pdf
See HW#7 for updated bonus problem.
12: Nov 9, 11 Markov Chains
Discrete-time Dynamical Systems
NO CLASS (Veterans Day) HW #8 [hw8.pdf] [hw8.tex] Due by 3pm on Fri (11/13)
SOLUTIONS: hw8-solns.pdf

Study Guide: ExamTopicsOverview.pdf
13: Nov 16, 18 EXAM (in-class)
Begin take-home Exam
14: Nov 23, 25 DUE: Take-home Exam Thanskgiving Week
15: 11/30, 12/2 SSA-in-class-logistic.R
16: Dec 7 Last Lecture NO CLASS (Prep Day) Project Instructions (project-report-outline.pdf) &
Templates (project-report-outline.docx; project-report.tex)
17: Dec 14 Final Meeting
(Project Presentations)