Spring 2010. Ordinary Differential Equations
(MAP 2302)
Instructor/office/contact info/office hours:
Instructor: Ognjen Milatovic Office: Building 14, Room 2733
Phone: 620-1745 E-mail:
Web page:
Office hours: Monday 3:15 p.m.- 5:15 p.m.;
Tuesday 10:00 a.m. - 11:00 a.m.;
Wednesday 3:15 p.m.- 5:15 p.m.;
Or by appointment
Prerequisites: MAC 2311 (Calculus I) and MAC 2312 (Calculus II)
Text:Nagle, Saff, Snider, Differential Equations & Boundary Value Problems,5thEd.
Calculator: You should have a graphing calculator or a scientific calculator.
Course Objectives:
This course is a one-semester introduction to ordinary differential equations with an emphasis on methods of solution. Throughout the course, we will consider various applications of ordinary differential equations.
Specific, measurable, manifestations of your understanding of the course material that will be tested during the semester include your ability to:
- understand the concept of slope field
- learn the techniques for solving separable, linear and exact equations
- understand basic mathematical models involving first-order differential equations
- solve applied problems using first-order differential equations
- learn the techniques for solving second-order linear differential equations with constant coefficients
- understand basic mathematical models involving second-order linear differential equations
- solve applied problems using second-order linear differential equations
- learn the techniques for solving higher-order linear differential equations with constant coefficients
- learn about Laplace transform and its properties
- use Laplace transform as a tool for solving differential equations
By the end of the semester, you should
- gain an appreciation of methods for solving ordinary differential equations and mathematical models involving such equations
- strengthen your skills in numerical and symbolic computation, mathematical reasoning, and mathematical modeling
- gain skills in learning and communicating mathematics
Attendance:
It is essential that you attend classes regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. You are responsible for finding out what material has been covered or what announcements have been made on days that you miss class.
Excused Absences or Late Work:
In order to turn in assignments late or to take make-up quizzes/tests, you must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mail message from your advisor saying that he/she believes that you should be allowed to make up work is acceptable.
Reading:
It is strongly recommended that you read the material from the textbook
ahead of time. Thus, when you then see the corresponding section covered in class, you will beable to follow along much more easily (as opposed to seeing the material for the veryfirst time in class).
Homework:
Homework will be assigned with each section. Although the homework will not
be collected, it is essential that you do homework exercises regularly: working these
exercises will help you get a solid grasp of fundamental concepts and techniques of
calculus and will increase your confidence as you proceed to learn new ideas.
Furthermore, questions on quizzes and tests will be very similar to assigned homework
exercises and the examples discussed during class. To help you work and understand
homework exercises, we will go over a limited number of homework exercises at the
beginning of each class.
While doing homework, do not just write down answers. Think about the problems posed, your strategies, the meaning of your computations, and the answers you get. It is often in this reflection that the greatest learning takes place. The main point is not to come up with specific answers to the specific problems you are working on, but to develop an understanding of what you are doing so that you can apply your reasoning to a wide range of similar situations.
Quizzes:
To ensure that you are keeping up with the homework, there will be several quizzes during the semester (roughly, one quiz every week). Some quizzes will be given in class, and some will be given as take-home assignments.
Class Participation:
Every class member will be expected to participate in class discussions. Your participation in class can be, for example, your contribution to course discussions and your contribution to answering in-class or homework questions. Please remember that your questions are a valuable part of our discussion of course topics.
Grading:
The final exam will count 25% of your course grade. Quizzeswill count 25% of your course grade. I will drop your worst quiz grade. Two in-class tests will together count 50% of your course grade (each test counts 25%). Course grades will be assigned as follows:
[90 - 100 %: A-, A], [80 – 89%: B-, B, B+],
[70 – 79%: C, C+], [60 – 69%: D],
[59% and below: F].
Cheating Policy:
Cheating is an insult to honest students – it will not be tolerated.
Course Topics:
Chapter 1 (Sections 1.1 – 1.3)
Chapter 2 (Sections 2.2 – 2.4)
Chapter 3 (Sections 3.2 and 3.4)
Chapter 4 (Sections 4.1 – 4.8)
Chapter 7 (Sections 7.2 – 7.7)
Chapter 5 (Sections 5.1 and 5.2)
Some sections may be omitted.
Important Dates:
January 18 (Monday) MLK Jr. Birthday
March 15—19 Spring Break (no classes)
March 26 (Friday) Deadline to Withdraw