Jacob Bernstein

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Math 306: Honors Differential Equations


Course Description

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.

Office hours:
Alex Grounds: Monday, 3-4 pm
Jacob Bernstein: Tuesday 3-4 pm or by appointment.

The syllabus is here.

References

The course texts are
  • M. W. Hirsch, S. Smale and R. Devaney, “Differential Equations, Dynamical Systems, and an Introduction to Chaos," 3rd Ed. (required)
  • W. Boyce and R. DiPrima, "Elementary Differential Equations and Boundary Value Problems," 10th Ed. (optional reference)

Exams

There will be three exams. Two in class midterms and a final.

The dates of the exams are
First Midterm: Wednesday, October 8.
Second Midterm: Wednesday, November 5.
Final Exam: Wednesday, December 17, 9am-12pm.

Computing

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.

(Tentative) Schedule

Week 1 (9/3): Basic Terminology and First Order Equations

Read: W 1.1-1.3, 2.1
No homework due.

Week 2 (9/8 & 9/10): Planar Linear Systems.

Read: M 2.1-2.5, W 2.6-2.7
Problem Set 1 due. Solutions.

Week 3 (9/15 & 9/17): Phase Portraits

Read: M 3.1-3.3, W 3.4, 4.1
Problem Set 2 due. Solutions.

Week 4 (9/22 & 9/24): Classification of Planar Systems and Higher Dimensional Linear Algebra.

Read M 4.2, W 5.1-5.3
Problem Set 3 due. Solutions.

Week 5 (9/29 & 10/1): Higher Dimensional Linear Algebra (cont.)

Read: M 5.4-5.6, W. 6.1-6.2
Problem Set 4 due. Solutions.

Week 6 (10/6 & 10/8): Higher Dimensional Linear Systems. First Midterm

Read: M 6.3-6.4
No homework due.
Practice Midterm.
Solutions to Midterm.

Week 7 (10/13 & 10/15 & 10/17): Non-Autonomous Linear Systems and The Laplace Transform.

Read M 6.5, W Handout (Section 4), Th: Handout (Sections 5.1-5.4)
Problem Set 5 due. Solutions. (Note: The original statement of 8(a) was wrong and could not be proved without additional assumptions. I've updated it with a correct statement.

Week 8: (10/20 & 10/22): The Laplace Transform (cont.)

Read: M Handout (Section 5.5-5.6) W Handout (Section 5.7)
Problem Set 6 due. Solutions. (Note: that there was a typo in problem 5b) -- an extra factor of 1/2pi was needed -- this has been corrected.

Week 9 (10/27 & 10/29): Non-linear Systems

Read: M 7.1-7.2, W 7.3-7.4
Problem Set 7 due. Solutions.

Week 10 (11/3 & 11/5): Non-linear Systems (cont.), Second Midterm

Read: M 8.1
No homework due.
Practice Midterm.
Solutions to Midterm.

Week 11 (11/10 & 11/12): Equilibria in Non-linear Systems;

Read: M 8.2-8.3, W 8.4-8.5
Problem Set 8 due. Solutions.

Week 12 (11/17 & 11/19): Global Non-linear Techniques

Read: M 9.1-9.2, W: 9.3-9.4
Problem Set 9 due. Solutions.

Week 13 : Thanksgiving Break

No Class

Week 14 (12/1 & 12/3): Epidemiological models; Proof of Local Existence and Uniqueness

Read M: 11.1, W: 17.1-17.2
Problem Set 10 due.

Final (12/17)

Checklist of topics we covered to help you study.
Practice Final.
Final Solutions.

Fall 2014 -- Department of Mathematics, Johns Hopkins University.