Coordinates:

Lectures: Allen Hall 103 MWF 10:00-10:50

Instructor: Bard Ermentrout

Office Hours: TBA
Office: Thackeray 502
Phone: 624-8324
EMAIL: bard@pitt.edu
WWW: http://www.pitt.edu/~phase

• Written homework 40%
• Project 20%
• Two Exams 40% (Take home)

The books are An Introduction to Mathematical Modeling by Edward A. Bender (Dover - really cheap; this is a super old school book), and Mathematical Modeling by Mark Meerschaert 4th edition

• 8/27-8/31 - What is Modeling (Bender, chapter 1) and Chapter 2 Arguments of scale , Bender
• HERE IS HOMEWORK 1 Due Friday Sept 7
• 9/5-9/7 (Labor day is a day off) Chapter 2, in Bender (dimensional analysis) and Chapt 1.1-1.3 Meerschaert
• HERE IS HW 2 Due Friday Sept 14
• 9/10-9/14 Chapter 1,2 in Meerschaert -- optimization
• 9/17-9/21 Chapter 3 in Meerschaert. If you have Excel or a similar spreadsheet, you should make sure to add on the "Solver" package since you can use this to solve the linear programming problems in HW4. I will also consult the following source Jeff Wheeler's notes on optimization
• HW 3 Due 9/21 Please solve problems 1,3,7 in Chapter 2.4 in Meerschaert. NOTE: In the whale problems, you *do not* have to solve the differential equations; all questions relate to the rates which are given.
• 9/24-9/28. We will finish chapter 3 in Meeschaert and begin Dynamical Modeling (Chapter 4)
• Homework 4 Due 9/28/18
• Introduction to dynamical and mechanistic modeling
  • Discrete time systems
  • Simple first order models and cobwebbing
  • Steady state analysis
  • Some extra notes on discrete systems 1 Don't do the HW in these.
  • Some extra notes on discrete systems 2
  • Some extra notes on discrete systems 3
• HOMEWORK 5, Due Oct 11
• Week of Oct 1 - we will continue with discrete dynamical systems
  • For any of you crazy enough to try it, this as an Excel simulation of the discrete predator prey model with output
  • This is same code in ODE format for XPP
  • For some of the homework, you will have to do a simulation and you can use either method, but eventually, you'll have to use something like my program XPP or matlab or other solid solvers
• Week of Oct 8. We will start ODE models. There will be no class Wed Oct 10 due to travel. Sorry!
• Some notes on mechanical models We will cover some of this material over the next week or so
• Homework due Friday Oct 19
• Week of Oct 15 I will finish up the mechanical models and also review some basic phase-plane analysis. We will learn mass action kinetics and I will apply tjis to different types of models
• Mid term exam will be given to you on October 22 and will be due Oct 27 in class. No exceptions, no emails of the exam. The exam will consist of a bunch of problems that are closely related to your homework: (Depending on time, I may give you a sample exam, but no promises)
  • Arguments from scaling
  • Dimensional analysis (Pi theorem)
  • Optimization in one and two variables with and without constraints
  • Linear programming
  • integer programming
  • Discrete dynamical systems
• Week of Oct 22 - more analysis of ODEs
• Midterm -- Due Friday Oct 26
• Here is the bird data for problem 1 in the midterm
• Week of Oct 29 - we will finish up ODE modeling
• HOMEWORK 7 Due Nov 2
• Here is some code for problem 4. Please note that I have not put the correct equations in since that is part of what the exercise asks for
• Week of Nov 5
  • Monday read Bender page 124-126
  • Wednesday - Friday Game Theory!!
  • HW 8 Due Nov 9
    • voter problem in matlab
    • waterwheel problem in matlab
    • voter problem in xpp
    • waterwheel problem in xpp
    • Note that HW8 contains a corrected version of problem 1 for HW 7
    • Some notes on game theory and other stuff
• Week of Nov 12 - just a little more Game Theory and then Meeschaert chapter on Probability models
• Homework 9 Due Nov 16
  • XPP File for replicator dynamics and RPS
  • Matlab file for replicator
• Week of Nov 19 and Nov 26. Chapter 7 and 8 in Meeschaert.
• Homework 10 -- Due Nov 30
• Depending on the number of Projects, we will devote either 2 or 3 days in the week of Dec 3 to presentations.
• Final exam will be Take home. I will give it to you Dec 10 and it will be due Friday Dec 14 by 5 PM EDT. (10 PM UTC) Here are the topics that will possibly be on the exam:
  • Euler-Lagrange and Mechanics
  • Law of mass action
  • Linear stability analysis and phase-plane modeling
  • Simulation of differential equations
  • Game theory
  • Probability models and some Markov chains

Project Order

• Wednesday Dec 5
  1. Stochastic Biology
  2. Newton's Cradle
  3. BBall - (Coyne et al)
• Friday Dec 7
  1. Catapult
  2. BBall - (Corman et al)
  3. Voting

FINAL EXAM

• Final Exam Due Friday Dec 14 5 PM EST -- answers will be accepted as hardcopy only!!!
• XPP code for problem 2
• Matlab code for problem 2

Answers to Fall 2018 Homeworks

1. HW 1
2. HW 2
3. HW 3
4. HW 4
5. HW 5
6. HW 6
7. HW 7/8
8. HW 9
9. HW 10

Additional Info

• Extremely brief Maple tutorial

• Differential equations using the computer

  • linear 2D systems
  • nonlinear 2D systems

• Project

  A central part of the course will be a project in which you choose some sort of physical, social, or biological system and create a mathematical model of it to explain some aspect of the system. For example, in the past, some students have looked at chemical oscillation models, some have modeled simple mechanical toys, some have modeled vampires. By the middle of the term, you should be thinking about a project. The project should have the following components:
  • Introduction to the problem
  • Approach to modeling
  • Model development and equations
  • Analysis and simulation (if appropriate)
  • Conclusions based on the analysis
  All totaled, should be about 3-5 pages including figures. You will give a 10 minute prsentation during the last week of class before FINALS. The project does not have to be original in that you can find a model in a paper as long as you show that you have done the analysis and simulations.

• Homework

  There will homework of several varieties. Much of it will be taken from the book but there will be a substantial amount of homework which you can do on the computer that will allow you to simulate different systems. I will describe these later on in the term, but they will likely involve your using the computer and your brains to solve some applied problems that arise in applications.

• Software

  XPPaut info I have not specified any particular software package to use for the course but I will introduce you to a piece of software that I wrote that allows you to solve and animate ODEs, PDEs, and all the kinds of equations you will encounter in the course. It is available for Mac, Windows, and Unix platforms and is free. Some of the problem may be easier with the use of software; I will introduce its use to you during the course of the semester. The software is available in some of the labs, but I can show you how to put it on your laptops. Since MATLAB is available (free or cheap for students), you are also encouraged to use that. Indeed, I will use it for linear programming when we cover that