Sections offered SPRING 2022:
#8557 |
PAOLO PIERSANTI |
TuTh 11:30 AM–12:45 PM |
BH 006 |
CLASS NOTES: COLL (CASE) N&M Breadth of Inquiry credit
Class meets In Person. For more information visit https://covid.iu.edu/learning-modes/index.html
Department Consent Required
Tentative Course Outline: The course constitutes the direct continuation of MATH-M/S 343. The course contents are divided into two parts.
Part 1: Linear Systems of Differential Equations. In this part, by closely following Chapter 7 of the main textbook, Logan Chapters 5.1–5.3 and 6, Kelley-Peterson Chapter 2, Greenberg Chapter 4 and Agarwal-O’Regan Chapters 17–19, we will describe the theory of systems of linear differential equations, including methods of solution (using linear algebra), geometry of orbits, etc.
Part 2: Nonlinear Systems of Differential Equations. In this part, by closely following Chapter 9 of the main textbook, Logan Chapters 5.4–5.5 and 7, Kelley-Peterson Chapter 3, Greenberg Chapter 7 and Agarwal-O’Regan Chapters 25–28, we will analyse non-linear systems of differential equations, including stability and Lyapunov methods. We will also present classical examples from mathematical biology such as competing species and predator-prey models, as well as periodic solutions to planar systems.
If time permits, we will also look at systems in higher dimensions including the Lorenz system and perhaps go into an introduction to two-point boundary value problems and Sturm-Louville systems (Chapter 11 of the main textbook, Kelley-Peterson Section 5.4 and Agarwal-O’Regan Chapter 36).