Instructor: Dr. Timothy Feeman :
Department of Mathematical Sciences, Villanova
University,
800 Lancaster Avenue, Villanova, PA 19085-1699 USA
Office: SAC373; Phone: (610) 519-4693 ;
e-mail link;
Fax:
(610) 519-6928
Class meetings schedule:
2705-001: MWF 11:30 am to 12:20 pm in Mendel G87; Tues.
1:00 pm to 1:50 pm in Mendel G88.
2705-003: MWF 12:30 pm to 1:20 pm in Mendel G87; Tues.
12:00 pm to 12:50 pm in Mendel G88.
Final Exams:
You must
attend the exam for your assigned section unless I have given you special
permission.
2705-001: Monday, December 14, from 10:45 am to 1:15 pm, in Mendel G87.
2705-003: Monday, December 14, from 1:30 pm to 4:00 pm, in Mendel G87.
Tentative test dates:
September 22, October 27, and December 1 (all on Tuesdays)
Once the basic elements of Calculus had been formulated (in the late seventeenth century by Isaac Newton and Gottfried Wilhelm von Leibniz), it became increasingly apparent that many interesting phenomena that involved continuous changes could be described mathematically in terms of derivatives. Thus, the study of differential equations was born. Integration (anti-derivatives) is the reverse process to differentiation, so it is not surprising that integrals play a major role in solving differential equations. Somewhat later, beginning only in the nineteenth century, mathematicians began to systematically study phenomena that behaved "linearly", generalizing the behavior of vectors. The concepts of matrix, determinant, and eigenvalue were developed and today serve as the foundation of Linear Algebra. The two fields of Differential Equations and Linear Algebra became linked when it was realized that certain types of differential equations and systems of such equations behaved in a linear fashion and, thus, could be solved with the tools of Linear Algebra.
In this course, we will see how all of this works at a basic level. We will study first-order differential equations, matrices, systems of linear equations, vectors, linear transformations, eigenvalues and eigenvectors, higher-order linear differential equations, and systems of linear differential equations. As much as possible, our study will be rooted in concrete examples and applications.
Prerequisite courses: MAT 1500 and MAT 1505, Calculus I and II.
The required text for the course is Differential Equations and Linear Algebra, third edition, by C. Henry Edwards and David E. Penney (published 2009, Prentice Hall). We will discuss much of Chapters 1 through 7. (See here for a detailed list.) I expect you to actually read the text, but not passively. This means that you should keep a pencil and paper at the ready to work through examples and problems raised in the text. Without this, the ideas will not sink in enough to become part of your everyday working knowledge.
We will use the computer algebra system Maple 13 in this course. No prior experience with Maple is needed -- we will discuss in class what you need to know about it.
We have an unlimited site license for individual users of Maple here at
Villanova. That means that you can download your own personal copy of Maple 13
onto your own computer. This is a great deal that your tuition helps to pay for.
So take advantage of it! To get you started, here is a link to the
Maple
resources page on the Math Department web site.
http://www.villanova.edu/artsci/mathematics/resources/maple/
Homework assignments:
As a general policy, one or two problems will be assigned at each class meeting to be
handed in at the next class meeting. Each such assignment will be worth a maximum of five
(5) points. Usually these problems will be found in the text. On occasion, more than two
problems might be assigned. (No assignments will be given on test days or holidays.)
Additional homework: Beyond the assignments to be handed in, I will assign a variety of additional homework problems each week. Though not graded by me, these problems should not be considered optional. The more you practice, the deeper your understanding will be.
Tests.
Three fifty-minute tests will be held in class during the semester. Tentative test dates:
September 22, October 27, and December 1 (all on Tuesdays).
No make-up tests will be given without prior notification.
Final Exam.
The course will conclude with a cumulative final exam to be held
as scheduled by the Registrar's office:
2705-001: Monday, December 14, from 10:45 am to 1:15 pm, in Mendel G87.
2705-003: Monday, December 14, from 1:30 pm to 4:00 pm, in Mendel G87.
You must
attend the exam for your assigned section unless I have given you special
permission.
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Your final grade will be determined based on the following:
Grading: A weighted score of at least 90% will earn a grade of A-minus or higher. A score of at least 60% is guaranteed a grade of D or higher.
last revised: 7-august-2009