List of Lectures and Reading Assignments 372T Spring 2006 Text refers to Edelstein-Keshet "Mathematical Models in Biology" Jan 26 Linear and Difference Equations, First order difference equations, Section 1.1-1.3 Jan 31 Linear difference Equations; Section 1.5-1.7 Problem 1 discussed on page 26 on segmented organisms. Feb 2 Complex roots of equations 1.8 Blood CO_2 and Ventilation (Problem 18 on page 34). Feb 7 Review of Matrices Section 1.4 Eigenvalues and eigen vectors Model 1 of section 3.1 on population models. Feb 9 Linear and non-linear difference equations,adjusting parameters, stability, 2.1-2.4 Model 2 of section 3.1. Feb 14 Periodic points, bifurcation diagram for the logistics equation, Section 2.5 Feb 16 Projects (discussion of possible projects by students) Feb 21 Systems of first order difference equations, stability, Sections 2.7-2.8. Feb 23 Systems applied to popluation biology Section 3.2-3.3. Feb 28: Exam (or quiz, if you like) March 2: Introduction to differential equations. How to use dfield and pplane and what they mean. Basic population models.Chapter 5, sections 1-4. Chapter 4 Section 1. March 7: Solving linear differential equations (section 4.8). March 9: More on solving systems of linear differential equation. Stability. March 11: .... March 30: The basic population models: Exponential growth, the logistics equation and the Allee effect. Chapter 6 section 6.1 April 4: A very breif discussion of population models with two species: Chapter 6 6.2-6.3 April 6: The law of mass action. Translating chemical reaction pictures into differential equations. Fast and slow reactions. Chapter 7, 6.1-6.3. April 11: Jesse Sweet will give a presentation on some of his REU work. April 13: April: