MATH 213: Ordinary Differential
Equations
TR
Instructor: Xiaoliang (Leon) Zhu
Zab 202A x3287
xzhu@wells.edu
Office Hours: Monday
TA: Abbie Corwin
TA Office Hours:
Monday/Wednesday,
Text: Kostelich and Armbruster. Introductory Differential Equations: From Linearity to Chaos, Addison-Wesley.
Prerequisites: MATH 112 or permission of the instructor.
Content: Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. A differential equation (DE) is an equation involving a variable t which can often be thought of as time, an unknown function x, and the derivatives of x. More meaningfully, a DE describes the relationships among a function and its rates of change. Such relationships often arise naturally in Physics, Chemistry, Biology, and Economics, as well as other areas of Math. The goal is to use such a relationship to find a formula for the unknown function. We will cover several techniques for solving certain DE's, use computers to find approximate solutions of other DE's, and study the general theory of DE's. Our use of the theory is twofold: It provides a context in which to understand solutions, and it helps us recognize when a computer estimate is inaccurate.
Basic Topics: (Chapters 1,2,3,4,5,6,7)
Calculus Review—derivatives and curve-sketching, antiderivatives, MVT, FTC
Differential Equations—equations, solutions, directions fields, models
1 order DE's—separation of variables, exponential growth, integrating
factors, applications
BEAUT—existence and uniqueness of solutions
Linearity—operators, superposition, factorization
2 order DE's—oscillatory motion and applications, undetermined coefficients,
variation of parameters
Systems of DE's—qualitative behavior and geometry
Linear systems—introduction, eigenvalues, eigenvectors, homogeneous solutions
Requirements: There will be written homework assignments usually consisting of problems from the text. Do not wait until the night before homework is due to look at it, since some problems may require a few days of thought or computer lab work. In addition there will be three tests, as well as the final exam (scheduled for 9-noon on Friday, May 18).
Grading: The rough grading scheme is given below.
Homework 40%
Tests 45%
Final 15%
Attendance
Although attendance is not mandatory, you will be at a serious disadvantage if you do not attend class, because this course requires a large amount of hand-on experience. Class absence does not excuse you from your responsibility.
Academic Honesty and
Honor Code
You are encouraged to work with each other collaboratively. This helps both the helper and the helped, and the helper often get more from such an exchange of ideas. However, you should only submit your own work. Don’t hand in anything copied from others that you don’t understand.
I take issues of academic honesty very seriously, and it is your and my responsibility to uphold the College's Honor Code. This means, among other things, that I will not hesitate to report my suspicions of dishonesty to the College.