Introduction
This course is a one-semester introduction to differential equations (The applet here has a second order equation with its solution shown. You can play around with the applet and see some different equations and their solutions.) with the use of linear algebra. We will begin with the solutions of equations involving only first derivatives, called first order differential equations. ( A first order problem with the solution available ) Even these can be very difficult. We will move on to second order equations, which are very useful in both mechanical and electrical problems. (Homogeneous second order equations with a worked out example ) Then we will study the method of Laplace transforms, a general way of solving many differential equations, with a look at equations involving impulses. ( Step Functions ) The linear algebra will follow with Gaussian elimination as the basis of our calculations and conceptual understanding. (Linear Algebra Toolkit by Przemyslaw Bogacki ) An introduction to eigenvalues and their application to linear systems of differential equations will complete the course. ( Eigenvalues and Eigenvectors: An Introduction by M. A. Khamsi)
In parallel with this progression through analytic methods, there is a sequence of four computer labs, Computer Labs in Ordinary Differential Equations by Robert McOwen , which are an essential part of this course. These numerical methods are essential to learn in today's technological world. They also contain valuable conceptual material which supports the analytical material. You should note that it is often impossible to solve problems analytically in engineering practice. Numerical methods are then used, and one should have a grasp of the basics, so when the technology returns an absurd answer you recognize this.
To understand some elementary methods for solving ordinary differential equations and to be able to implement those methods. In this context, to gain an understanding of the modeling of physical systems through the use of differential equations.
To gain an understanding of the rudiments of the linear algebra.
To understand the use of linear algebra in solving systems of differential equations
Leonhard Euler and Jacob Bernoulli
You can see more at the web site Images of Mathematicians on Postage Stamps
Grades and Organizational Stuff
The instructor reserves the right to change this syllabus according to the needs which may arise in this class during this semester. Students are responsible to be aware of what goes on in the classroom including the announcement of exam dates, material to be covered on exams and any adjustments to this syllabus. If you have any questions that you are not comfortable asking in class please feel free to ask me after class or come to my office hours.
If I am unavailable or you wish to speak with someone else about this course, you should contact the
Chairman of the Mathematics Department, Professor Robert McOwen. Professor McOwen's office is 505 Lake Hall, his telephone number is 617-373-5635 and his e-mail address is mcowen@neu.edu
We will have quizzes on Thursdays, at the start of the class, every week. I will go over the material for the Thursday quiz in class on the preceeding Wednesday.
The average of these quizzes will acount for 25% of your grade in this course.
We will have one hour exam during the fourth week of the course, on Thursday, July 27th.
This hour exam will count as 20% of your grade in this course.
You will complete four computer lab assignments. NO LATE COMPUTER LABS WILL BE ACCEPTED.
The average of these labs will count as 15% of your grade in this course.
Please take note that some of the problems, homework and other, in this course, are lengthy but not so difficult. Since we are on a six week track, we will not be able to complete all of these in class. If you have difficulty with the homework, IT IS ESSENTIAL THAT YOU COME IN EARLY AND OFTEN TO OFFICE HOURS.
The two hour, common, commonly graded, final exam will count as 40% of your grade in this course.
Departmental Policies
Excused Absences or Late Work:In order to turn in assignments late or to take make-up quizzes and tests, students 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 they believe that you should be allowed to make-up work is acceptable.
Cheating is an insult to honest students:It will not be tolerated. The University's cheating policy and related disciplinary actions are detailed in the Student Handbook; the Handbook also includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited to): looking at the papers of others during a quiz or test, talking to other students during a quiz/test, looking at notes during a quiz/test (unless it is specifically announced that you may), copying other students' work outside of class, and obtaining help from others on take-home tests.
In this class, working together on homework is NOT considered cheating. Please be aware that this policy on working together outside of class varies greatly from one course to the next; the policy on what is allowed, that has been described in this paragraph, may well be considered cheating in your other classes.
The use of advanced calculators is NOT considered cheating in this course. Be aware, however, that other courses may well have a policy barring such calculators. Also, your instructor reserves the right to decide on the spot between what constitutes a "calculator" and what constitutes a full-fledged "computer".
All incidents of cheating will be reported to the Office of Judicial Affairs.
If you have any questions as to what constitutes cheating, please ask me.
Attendance:It is essential that you attend class 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. Students are responsible for finding out what material has been covered or what announcements have been made on days that they miss class.
Please note that we will treat you as an adult here. If you must miss a class, be late or leave early, it is expected, as polite behavior, that you will contact the instructor involved ahead of time and reach an agreement. This sort of behavior goes a long way when you have to miss a quiz, for instance. If you do not do this, the ball is in your court to make up work or use the missed quiz as the quiz which you drop.
Schedule of Topics and Assignments
The following table includes a calendar with homework problems to be covered.
They may change as we progress through the course.
