Applied Linear Algebra
General Information:
•Office hours: as posted or by appointment (check with me
in class, call, or send email).
•Prerequisite: MA 232 (or MA 132 and familiarity with matrix algebra).
•Required Text: Introduction to Linear Algebra (fifth edition) by Johnson, Riess,
and Arnold
(Addison-Wesley, 2002).
•Optional Supplement: Student's Solutions Manual.
•Time/Place: 10:00-10:50a.m. Monday, Wednesday, Friday in Science Center Lecture
Hall 362.
•Attendance: You are expected to attend class.
Homework:
Homework will be collected in class approximately once per week. The purpose of
homework is to help you
learn (not to test what you know); your homework score will reflect primarily
whether or not you did the work.
Many problems will have answers in the back of the textbook; it is your
responsibility to check your own
answers (and to ask for help when needed). Some problems may be graded in
detail; if I can't easily read or
follow your solutions you will not receive credit. The solutions you hand in
should include your work--not just
the final answers. You must do your own work.
Several homework projects involving MATLAB will be assigned; these may be
completed individually or in
teams as announced. No collaboration allowed between teams.
Quizzes:
Quizzes may be given in class with or without prior notice. Missed quizzes will
not be made up. Quiz problems
will typically be similar to assigned homework problems or test knowledge of key
definitions.
Exams:
There will be three hour exams, tentatively scheduled for Fridays 8 February, 7
March, and 11 April (in class).
The final exam (week of 28 April) will cover the entire course. No grade
exemptions from the final exam. If you
want me to reconsider your score on an exam problem, you must return the exam to
me--with a written
explanation of your request--within three days of when the exams are returned in
class.
Late Work:
All work is due when stated and will not be accepted late; missed quizzes and
exams will not be made up.
Exceptions may be made at my discretion in exceptional circumstances.
Grades:
Your final score will be a weighted average of your scores on homework problems,
projects, and quizzes (20%),
three hour exams (20% each for two highest, 15% for lowest), and final exam
(25%). Final scores translate into
letter grades by the scale 90-100 A, 80-89 B, 70-79 C, 60-69 D, 0-59 F with no
"curve".
Code of Ethics:
I take the Clarkson Code of Ethics seriously. Any
violation will result in a score of zero on the work in question
(at best) and will be reported to the Academic Integrity Committee. Cheating on
an exam will result in an F for
the course. For more information, see the section on Academic Integrity in the
Clarkson Regulations. When in
doubt, ask me in advance.
Course Learning Objectives:
•To learn the fundamental concepts of linear algebra in the concrete setting of
Rn
•To learn to use linear algebra to solve problems from engineering and other
fields
•To learn to use computer software to apply the techniques of linear algebra
Course Outcomes:
Upon successfully completing this course you should be able to:
•perform basic matrix calculations
•use matrices to solve systems of linear equations
•find least-squares solutions of linear systems
•set up and solve linear systems in applied problems
•explain the basic concepts of linear algebra (subspace, span, linear
independence, basis, dimension)
•identify and work with these concepts in Rn
•find an orthonormal basis for a subspace
•identify a linear transformation and find and use its matrix representation
•compute determinants of matrices
•compute eigenvalues and eigenvectors of matrices
•use eigenvalues and eigenvectors to diagonalize matrices and to solve systems
of linear ODEs
•use MATLAB to solve problems involving linear algebra
In order to achieve these outcomes you should expect to
spend about six hours per week reading and working
homework, in addition to the three hours per week in class.
Topical Outline:
Matrices and Systems of Linear Equations [chapter 1]
1. Solution of linear systems
2. Matrices and matrix algebra
3. Linear independence
4. Matrix inverses
2. Vectors in 2-Space and 3-Space [chapter 2]
3.The Vector Space Rn [chapter 3]
1. Subspaces
2. Basis and dimension
3. Orthogonal bases
4. Linear transformations
5. Least-squares problems
4.The Eigenvalue Problem [chapter 4]
1. Determinants
2. Eigenvalues and eigenvectors
3. Diagonalization
4. Application to differential equations