# Course Syllabus for Applied Linear Algebra

**General Information:**

**• Professor: **Scott R. Fulton (367 Science Center, 268-2379.).

**• Office hours:** as posted or by appointment (check with me in class, call,
or send email).

**• Course website:** See Blackboard for assignments, announcements, and other
information.

**• Prerequisite :** MA232 (or MA132 and familiarity with matrix algebra).

**• Required Text:** Linear Algebra and its Applications (third edition
update) by David C. Lay (Pear-

son/ Addison Wesley , 2006, ISBN 0-321-28713-4). This book comes with a CD
containing additional

information (Study Guide, solutions , data les, projects, etc.) you will need for
this class.

**• Time/Place: **2:00{2:50pm Monday, Wednesday, Friday in Science Center 160.

**• Attendance:** You are expected to attend class.

**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.

If you miss a quiz due to an excused absence, it will be dropped from your quiz
average.

**Exams: **There will be three hour exams, tentatively scheduled for
Wednesdays 16 September, 14 October,

and 11 November (in class). The final exam (week of 7 December) 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 least- squares 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 assign-

ments (reading and exercises) and projects, in addition to the three hours per
week you spend 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) The LU factorization

(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 Gram-Schmidt process

(d) Least-squares problems and applications

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