Math 356/756, Elementary Differential Equations


Time and place: WF, 10:05am - 11:20am, Biological Sciences 130.

Instructor: Wei Zhu (zhu at math.duke.edu).

Office hours: M, 1:00pm - 3:00pm, Gross Hall 351.

Textbook: Differential Equations with Boundary Value Problems, by Polking, Boggess, and Arnold, second edition. We will cover much of Chapters 1, 2, 3, 4, 8, 9, 10, 12, 13.

Homework: Homework is assigned every week (see the end of this page for the homework problems), and will be collected in class on Thursdays. Further information is given below.
  • No late homework will be accepted, but two lowest scores will be dropped.
  • Write your name and ID number at the top of the first page.
  • Staple your pages.
  • You can collaborate on the homework, but the final version must be written in your own words. Copying the solutions of others is strictly forbidden.
Exams: There will be a midterm and a final exam. The date of the midterm is October 16. The date of the final is December 12.

Grades: Homework 20%, midterm 35%, final 45%.

Syllabus: The following table will be updated as we proceed.

Lecture Date Book Sections Topics
1 8/28 1.1-3, 2.1 Derivatives, integrals, first-order ODE, normal forms, IVP, direction field.
2 8/30 2.2, 2.4 Separable equations, linear equations, integrating factor, variation of parameters.
3 9/4 2.3, 2.5 Models of motion, linear/quadratic air resistance, terminal velocity, scaling, mixing problems
4 9/6 2.6 Differential forms, integral curves, exact differential equations.
5 9/11 2.6, 2.9 Integrating factors, homogeneous equations, autonomous equations, equilibrium points and solutions.
6 9/13 2.9, 2.7 Phase line, stability, existence/uniqueness of solutions, application of uniqueness theorem.
7 9/18 4.1 Second order (linear) ODE, structure of the general solutions, Wronskian.
8 9/20 4.3, 4.4 Linear, homogeneous equations with constant coefficients, harmonic motion, undamped harmonic motion, amplitude and phase.
9 9/25 4.4, 4.5 Damped harmonic motion, methods of undetermined coefficients.
10 9/27 4.6, 4.7 Variation of parameters, forced harmonic motion.
11 10/2 8.1-4 ODE systems, vector notations, geometric interpretation of solutions of an ODE system, phase space plots, direction field, existence and uniqueness, linear systems.
12 10/4 8.5, 9.1 Linear independence and dependence, Wronskian, linear systems with constant coefficients, eigenvalues/eigenvectors.
13 10/9 9.2 Planar systems, Four different cases for solving planar systems.
14 10/11 N/A Review
15 10/16 N/A Midterm
16 10/18 9.3, 9.4 Phase plane portraits, the trace-determinant plane.
17 10/23 9.5 Higher-dimensional systems, algebraic/geometric multiplicity.
18 10/25 9.6 Exponential of a matrix, trunction, generalized eigenvectors and the corresponding solutions, the solution procedures (for high-dimensional homogeneous linear systems with constant coefficients.)
19 10/30 9.6, 9.7 The solution procedures (for high-dimensional homogeneous linear systems with constant coefficients,) qualitative analysis of linear systems
20 11/1 9.7-9 Higher-order linear equations, structure of the general solution, fundamental set of solutions (for higher-order homogeneous differential equation with constant coefficient,) inhomogeneous linear systems.
21 11/6
22 11/8
23 11/13
24 11/15
25 11/20
26 11/22
27 12/4
28 12/6


Homework problems: