MA 117: Difference Equations and Linear Algebra (3 cr)
Fall 2003, 9:00 - 9:50 MWF, SH 110
Instructor: Dr. Kelly Cline
E-mail: kcline@carroll.edu
Office: SH 119
Office phone: 447-4451
Office Hours: MWF 2-3, TR 9-11, or by appointment.
Course Description:
This is an introductory college mathematics course in finite difference equations
and linear algebra. Topics include sequences, differences, linear
and nonlinear difference equations, systems of difference
equations, numerical solutions of linear and nonlinear equations,
and analytical techniques for solving linear systems using linear algebra.
Applications from many fields are studied and the role of
mathematical modeling is a central focus. Formal computer labs
are a part of the course each week, with spreadsheets being the
primary software employed. This course satisfies a general liberal
arts requirement for all students and the mathematics requirement
for business majors. Prerequisite: three years of high school mathematics
through Algebra II.
Textbook:
Discrete Dynamical Systems: Mathematics, Methods, and Models by Arney, Giordano, and Robertson.
Grading:
Homework and In Class Work: 20%
Labs: 15%
Exam 1: 15%
Exam 2: 15%
Exam 3: 15%
Final Exam: 20%
There will be four exams in this class, a midterm covering Chapter 1 on Wednesday, September 17,
a midterm covering Chapter 2 on Monday, October 27, a midterm on Friday, Nobember 21, and a final
at the end of the term. In order to pass this class, all students
must take all four exams.
I will use a no-curve grading policy to assign final grades:
above 90% = A, 80% - 89% = B, 70% - 79% = C, 60% - 69% = D, below 60% = F.
Homework:
There will be homework due at the beginning of almost every class.
I will not accept any late homework unless you make some arragement with
me before the class period when the homework is due. I will drop your
two lowest homework scores, so you can miss two homeworks without any penalty.
In Class:
I will assign a section of the text for you to read before each class.
Rather than lecturing, I prefer to ask you questions about what we've read, and guide
a class discussion about the material, so if you haven't done the reading it is very
obvious! There will also be many short assignments that you will do in small groups
during class. Often these will require a calculator so always bring one with you to class.
Labs:
Thre are lots of things that you can do with pencil and paper, or with the help of a calculator. But
using computers can make your work much more powerful. So we will meet in the computer lab (Fortin 115)
almost every Friday, so that you can use Excel, a spreadsheet program, to do lab project that would
take way too much time to do just with pencil and paper. You may do the lab individually or in
groups of two. One week after we do the lab, you must turn in a lab report answering all the questions
in the lab, and briefly explaining what you did. This lab report must be typewritten and
professional in style.
Tentative Schedule
|
Topic |
Assigned Reading |
Date |
|
Introduction to the Course |
|
M 8/25 |
|
Mathematical Modeling |
1.1 |
W 8/27 |
|
Lab 1: Calculating Interest |
|
F 8/29 |
|
Modeling Change with Difference Equations |
1.2 |
W 9/3 |
|
Lab 2: Data and Proportionality |
|
F 9/5 |
|
How to Determine Stability |
1.3 |
M 9/8 |
|
Equilibrium Values |
|
W 9/10 |
|
Lab 3: Mortgages and Credit Cards |
|
F 9/12 |
|
Chapter 1 Review |
|
M 9/15 |
|
Chapter 1 Examination |
|
W 9/17 |
|
Analytic Solutions |
to 2.1.2 |
F 9/19 |
|
Testing Solutions |
2.1.3 |
M 9/22 |
|
Finding Solutions |
2.1.4 |
W 9/24 |
Lab 4:
 |
|
F 9/26 |
|
First Order Linear Systems |
2.2 |
M 9/29 |
|
Solving First Order Linear Systems |
|
W 10/1 |
|
Lab 5: Exponential Decay |
|
F 10/3 |
|
Nonhomogeneous Equations |
2.3 |
M 10/13 |
|
Exponential Functions |
2.4 |
W 10/15 |
|
Polynomial Functions |
2.5 |
F 10/17 |
|
Long Term Behavior |
2.6 |
M 10/20 |
|
Applications |
2.7 |
W 10/22 |
|
Chapter 2 Review |
|
F 10/24 |
|
Chapter 2 Examination |
|
M 10/27 |
|
Modeling and Classifying Systems |
3.1 |
W 10/29 |
|
Lab 6: Populations |
|
F 10/31 |
|
Numerical Solutions of Systems |
3.2 |
M 11/3 |
|
Nonlinear Models |
7.1 |
W 11/5 |
|
Lab 7: Rabbits and Owls |
|
F 11/7 |
|
Numerically Solving Nonlinear Models |
7.2 |
M 11/10 |
|
Systems of Algebraic Equations |
4.1 |
W 11/12 |
|
Lab 8: Yellowstone Bison |
|
F 11/14 |
|
The Augmented Matrix |
4.2 |
M 11/17 |
|
Review |
|
W 11/19 |
|
Examination Ch 3, 7, 4 |
|
F 11/21 |
|
Matrices: Properties and Operations |
4.3 |
M 11/24 |
|
Square Matrices: Inverses and Determinants |
4.4 |
M 12/1 |
|
Matrix Equations and Their Solutions |
4.5 |
W 12/3 |
|
Lab 9: Fun With Linear Algebra |
|
F 12/5 |
|
Linear Dynamical Systems of Several Variables |
5.1 |
M 12/8 |
|
Applications of Linear Dynamical Systems |
|
W 12/10 |
|
Review |
|
F 12/12 |
|
Final Examination |
8:00 - 9:45 a.m. |
M 12/15 |
Kelly Cline
2003-08-22