Course Page for Math 331.1 - Fall 2009
Ordinary Differential Equations for Scientists and Engineers
- Instructor:
- Bruce Turkington, Professor
LGRT 1423K
turk@math.umass.edu
www.math.umass.edu/~turk
- Office Hours:
- Tues. 10:00---12:00, Wed. 2:00---4:00, and by appointment
- Lectures:
- Mon., Wed., Fri. 11:15---12:05 in LGRT 219
- Text:
- Elementary Differential Equations (8th edition) ,
by W.E. Boyce and R.C. DiPrima
- Teaching Assistant:
- Sami Zreik
Office: LGRT 1337
Office Hours: Tues 12:00---1:30, Thurs 12:00---2:30
Email: zreik@math.umass.edu
Prerequisites for this course:
Calculus I,II. That is, a thorough knowledge and
understanding of differential and integral calculus in one variable.
Some acquaintance with the basic notions of physical science, for
the purposes of motivating and applying differential equations.
Topics covered in this course:
- Introduction to DEs -- Chapter 1. Sections 1.1 to 1.4
- First-order ODEs -- Chapter 2. Sections 2.1 to 2.4
- Second-order ODEs -- Chapter 3. Sections 3.1 to 3.9
- Applications of ODEs -- Chapter 2. Sections 2.3, 2.5.
Chapter 3. Sections 3.8,3.9
- Laplace transform technique -- Chapter 6. Sections 6.1 to 6.6
- Basic numerical solutions of ODEs -- Chapter 8. Sections 8.1,8.2,8.3
(as time permits)
Course objectives and approach:
Differential equations (DEs) form the backbone of mathematical
modeling throughout modern science. They are important and
interesting because they are the expression of physical, biological,
economic or other laws, whenever those laws concern the rates of
change of interrelated variables. For instance, DEs describe
mechanical oscillations, chemically reactions, electrical circuits,
ecological population dynamics, and much more.
In this course we study only ordinary differential equations,
which are DEs whose unknowns depend on one variable. Most
often the independent variable represents time. But the dependent
variable(s) may represent all sorts of different things.
We mainly concentrate on how to solve those ODEs which arise
frequently in science and engineering. For most of the course we
consider scalar ODEs that govern one unknown function, and we study
separately those involving only the first-derivative of the unknown
function and those involving also the second-derivative. This is our
core material. As time permits at the end of the course we consider
systems of ODEs that govern several unknown functions, and we develop
the basic linear algebra needed to investigate them.
We concentrate on methods of solving ODEs, not general theory or
qualitative behavior. Basically there are three types of approaches
to the analytical solution of elementary ODEs: (1) Integration
techniques; (2) Trial function techniques; and (3) the Laplace
transform. We will cover all these techniques in detail.
We will only consider numerical methods very briefly
in this course, even though
they are important whenever analytical techniques are not available.
They are discussed in detail in another course, Math 551. The
textbook comes with a CD that works on Microsoft operating systems
and which can be used to illustrate solutions, if the student
wishes. Some of the textbook's problems use the computer package in
the CD. But our discussion and our assigned problems will not
require the use of this computer package.
Grading procedure:
- Final Exam[120 minutes]: 40%
Time and place: As dictated by University Exam Schedule for Fall09.
- 1 Midterm[75 minutes]: 20%
Date: In class, Monday, November 2.
- 6 biweekly quizzes[20 minutes]: 20% (lowest score dropped)
Dates: Mondays -- Sept. 21, Oct. 5, Oct. 19, Nov. 9, Nov. 23, Dec. 7
- Graded WebWork homework, assigned regularly: 20%
Homework
Homework problems will be assigned regularly as we cover each section
in the text. They will be completed on the WebWork system. Logistic
details will be given in class; otherwise see instructor for a username
and password.
It is essential to do a variety of problems when learning mathematics.
Reading ahead:
Always keep up to date with your reading and re-reading of the
textbook. It should be clear which section we are going to discuss
each day of class, and you are strongly encouraged to read that section
before the class. That way you will get the most out of
our presentation and discussion. Then shortly after class
you should re-read the section in the textbook to ensure your
understanding.
Recommended practice problems for midterm exam:
Section 2.1 # 5c, 11c, 15
Section 2.2 # 3, 7, 9, 13
Section 2.3 # 5, 11
Section 2.5 # 21, 23
Section 2.6 # 3, 9, 15
Section 3.1 # 3, 7, 13, 17
Section 3.2 # 21
Section 3.4 (3.3 in 9th ed) # 7, 11, 25
Section 3.5 (3.4 in 9th ed) # 3, 11
>h3> Recommended practice problems for final exam:
[Note: the final exam is comprehensive, and so the above recommended
problems for the midterm still apply to the final.]
Section 3.6 (3.5 in 9th ed) #2, 3, 6, 7, 14, 17
Section 3.7 (3.6 in 9th ed) #6, 11, 12
Section 3.8 (3.7 in 9th ed) #21, 24
Section 3.9 (3.8 in 9th ed) #18, 19
Section 6.1 # 5, 10, 16
Section 6.2 # 4, 5, 6, 13, 14, 20, 22
Section 6.3 # 7, 9, 14
Section 6.4 # 2, 4, 6
Section 6.5 # 2, 6, 11
Section 6.6 # 15, 17
Problem set for Applications of Second-order DEs:
Hand in written solutions on or before Wed. Nov. 25.
Section 3.8 (old editions), 3.7 (9th edition) [Mechanical and Electrical
Vibrations] : # 3, 13, 19, 26
Section 3.9 (old editions), 3.8 (9th edition) [Forced Vibrations] :
# 4, 17, 18