1. Exam 2 Review

2. Review The final exam will be comprehensive. It will cover material in the text book from Chapters 1 – 6. It will also cover material not in the text book that was provided to you in the lecture notes. Please see the Exam 1 review for what to expect from chapters 1 -- 6.2 –All of that information still applies

3. Review – Discrete Models Exam 1 –Covered some mathematical and graphical aspects of discrete equations (problem 1) Exam 2 –Will likely cover modeling aspects of discrete equations Model development, analysis, and interpretation

4. Review – Continuous Models Exam 1 –Covered some model analysis and interpretation for single-species continuous equations (problem 2 - Harvesting) Exam 2 –This is also fair game for Exam 2 Instead of leading you through the mathematics, I may ask you a biological question and you will need to decide what mathematics to do to answer that question

5. Review – Continuous Models Exam 1 –Covered the analysis of a system of two equations (problem 3) Exam 2 –This is also fair game for Exam 2 –Some items that were not on Exam 1 that will very likely be included on Exam 2 are: Nondimensionalization Produce a phase portrait – by hand Produce a bifurcation diagram

6. Review – Continuous Models Exam 1 –No model development Exam 2 –This is fair game for Exam 2 From the description of a biological problem, you should be able to derive a system of equations to model it –We’ve had several group modeling sessions to practice this skill

7. Review Continuous Models Exam 1 –No computational component Exam 2 –This is fair game for Exam 2 –Be comfortable writing MATLAB code that solves single ODEs as well as systems of two or more equations –NO pplane

8. Review – Specifics Chapter 6: 6.1 – 6.4 and 6.6 –Interacting Species Predator-Prey (Lab 5, Ch 6.2) Competition (Chapter 6.3 Assigned Reading) –Multiple Species Models Lecture notes and chapter 6.4 –SIR Models (Ch 6.6 and lecture notes) Be able to recognize, develop, analyze and interpret the results from these types of models

9. Review - Specifics Multispecies Model Analysis –Jacobian Matrix of Partial Derivatives –Characteristic Polynomial –Stability Criteria Routh-Hurwitz Criteria – Chapter 6.4 page 234

10. Review – Specifics SIR Models –Model development –Model reduction –Conditions for an epidemic –Properties of an epidemic Severity How many get infected etc