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Applied Linear Algebra
Assignments: The work you do outside class will play a major role in
helping you learn the material for
this class. Read the assigned section—and work all practice problems—before
coming to class each day.
After covering the material in class, work the assigned exercises, check your
answers (in the back of the
text and/or the Study Guide), and ask for help when needed. Homework will not be
handed in (unless
otherwise announced) but will be reviewed in class as needed. Most quiz and exam
problems will be taken
from the textbook examples, practice problems, and assigned exercises (possibly
with minor modifications).
Projects: Several projects involving the use of MATLAB will be
assigned; these projects may be completed
individually or in teams as announced. No collaboration allowed between teams.
Quizzes: Quizzes may be given any day in class without prior notice. Missed quizzes will not be made up.
Exams: There will be three hour exams, tentatively scheduled for
Wednesdays 4 February, 4 March, and
8 April (in class). The final exam (week of 27 April) will cover the entire
course. No grade exemptions
from the final exam. If you want me to reconsider your score on an exam, you
must return it to me—with
a written explanation of your request—within three days of when the exams are
returned in class.
Late Work: Projects are 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
quizzes (10%), projects and any
other work handed in (15%), three hour exams (20% each for two highest , 15% for
lowest ), and final exam
(20%). 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 a grade of 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 R^{n}
• 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
• set up and solve linear systems in applied problems
• identify a linear transformation and find and use its matrix representation
• explain the basic concepts of linear algebra (subspace, span, linear
independence, basis, dimension)
• identify and work with these concepts in R^{n}
• compute determinants of matrices
• compute eigenvalues and eigenvectors of matrices
• use eigenvalues and eigenvectors to diagonalize matrices and to solve systems
of differential equations
• find an orthonormal basis for a subspace
• find leastsquares solutions of linear systems
• use MATLAB to solve applied problems involving linear algebra
In order to achieve these outcomes you should expect to
spend about six hours per week doing the assignments
(reading and exercises) and projects, in addition to the three hours per week in
class.
Topical Outline:
1. Systems of Linear Equations [chapter 1]
(a) Row reduction and echelon forms
(b) Vector and matrix equations
(c) Linear independence
(d) Matrices and linear transformations
(e) Applications of linear systems
2. Matrix Algebra [chapter 2]
(a) Matrix operations
(b) The inverse of a matrix
(c) Partitioned matrices
(d) Matrix factorizations
(e) Subspaces of R^{n}
(f) Basis, dimension, and rank in R^{n}
3. Determinants [chapter 3]
4. The Eigenvalue Problem [chapter 5]
(a) Eigenvalues and eigenvectors
(b) Diagonalization
(c) Discrete dynamical systems
(d) Applications to differential equations
5. Orthogonality and Least Squares [chapter 6]
(a) Inner product , norm, and orthogonality
(b) Orthogonal vectors and projections
(c) The GramSchmidt process
(d) Least squares problems and applications
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