Math 306: Honors Differential Equations
This course is an honors introduction to differential equations. We will cover most of the material from the standard course as well as some additional topics. Our primary focus will be on studying linear systems and then using this knowledge to study the qualitative behavior of non-linear systems.
Lectures are Monday and Wednesday 12-1:15 PM in Krieger 308. Section meets Friday 12-12:50 PM in Krieger 308.
Problem sets will be due in class on Wednesdays -- see the schedule below for dates. No late homework will be accepted. The lowest homework grade will be dropped.
The syllabus is here.
ReferencesThe course texts are
ExamsThere will be three exams. Two in class midterms and a final.
While not essential to the course, being able to plot solutions with the help of a computer can greatly assist in your understanding. As a Hopkins student you are entitled to a free copy of Mathematica which has all the tools (and more!) to do so. Instructions on how to obtain your copy are here. If you want to use something with a less steep learning curve, you can find an online java applet which plots slope fields and solutions is here. See this page if you are having problems running the applet.
Week 1 (9/3): Basic Terminology and First Order Equations
Week 2 (9/8 & 9/10): Planar Linear Systems.
Week 3 (9/15 & 9/17): Phase Portraits
Week 4 (9/22 & 9/24): Classification of Planar Systems and Higher Dimensional Linear Algebra.
Week 5 (9/29 & 10/1): Higher Dimensional Linear Algebra (cont.)
Week 6 (10/6 & 10/8): Higher Dimensional Linear Systems. First Midterm
Week 7 (10/13 & 10/15 & 10/17): Non-Autonomous Linear Systems and The Laplace Transform.
Week 8: (10/20 & 10/22): The Laplace Transform (cont.)
Week 9 (10/27 & 10/29): Non-linear Systems
Week 10 (11/3 & 11/5): Non-linear Systems (cont.), Second Midterm
Week 11 (11/10 & 11/12): Equilibria in Non-linear Systems;
Week 12 (11/17 & 11/19): Global Non-linear Techniques
Week 13 : Thanksgiving Break
Week 14 (12/1 & 12/3): Epidemiological models; Proof of Local Existence and Uniqueness