Introduction to Linear Algebra (3 units)

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```					SYLLABUS          MATH 254 Sect. No. 01         Fall ‘04   Class No. 5341       page 1 of 3
Introduction to Linear Algebra (3 units)
Class Location and Times:    T Th 12:00noon - 1:20pm in Room 704B

Prerequisites: A grade of “C” or higher in Math 251.

Course description: Introduction to linear algebra including: matrix algebra, Gaussian elimination,
determinants, vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors.

Instructor: Mimi Grifkin      Office: Rm 320C Phone: (619)421-6700 x5871
Office Hours: MWF 11 − 11:50am, Tues. 1:30 − 2:20pm , Thurs. 11 – 11:50am
e-mail: mgrifkin@swc.cc.ca.us      Mailbox: Rm. 345 (Math, Science and Engineering Office)

Textbooks and Materials:
1) Elementary Linear Algebra, 5th Edition, by Larson and Edwards
2) Student Solutions Guide, by Bruce Edwards
3) TI-83 PLUS graphing calculator (or equivalent, such as: TI-82, TI-83, TI-85, TI-86)

Midterms (3) (1500 pts)                              =       3/6 of final grade
Comprehensive Final Exam (1000 pts)                  =       2/6 of final grade
6/6 (3000 pts)

Your two (2) lowest quiz scores will be dropped. Take-home quizzes due at the
beginning of first hour of class, NO exceptions. (We will
alternate between in-class and take-home quizzes.)

A diagram of the grading is shown here:

Final Exam is scheduled for this class at: Tues., December 14, 10:30am - 12:30pm
Please note: If you get 50% OR LESS on the Final, you will not pass the class even if your overall
grade is passing! No Make-Up Quiz or Exam will be allowed for any reason. Late assignments not
accepted. Grades will be decided by the standard 90%=A, 80%=B, 70%=C,... etc., unless a curve is
deemed appropriate by instructor. The average on the curve will be equal to a “C” grade. All backpacks
and cell phones must be placed by the door on test days. No bathroom breaks during exams. (No
exceptions, except pregnant women.) No hats or sunglasses during exams. No extra time allowed for
exams.

Homework is assigned daily, but not collected. It is strongly recommended that students keep up with
their homework in order to maintain their day-to-day understanding of the material. Doing about 6 hours
a week is a reasonable amount.

Cheating and other inappropriate student behavior: Appropriate disciplinary action will be taken,
which may include, (but is not limited to): a grade of “F” on that assignment, a letter to Dean of Math,
Sciences, and Engineering, Dean of Student Activities, and/or the Vice President of Academic Affairs,
exclusion from class, a grade of “F” for the course, academic probation, expulsion from the college.
SYLLABUS             MATH 254 Sect. No. 01             Fall ‘04 Class No. 5341               page 2 of 3
Drop info: (Provided for your info ONLY - Please check Fall Schedule for validation) Last day to drop and get a refund:
August 27. Last day to drop without receiving a “W”: September 10 at 3pm. Last day to file for Credit/No Credit: Sept. 10 at
3 pm. Last day to drop and get a “W”: November 5 at 3pm.

Special Needs: Students with disabilities who may need academic accommodations should discuss options with instructor
during the first two (2) weeks of class. An alternate form of this syllabus and other class handouts is available upon request.

Attendance: Attendance is taken daily. Attendance will not be considered as part of your grade, except: (Please see page
17 in Course Catalog for school’s Excessive Absence/Tardiness policy.)

(a) If you are absent for two-week’s worth of classes (4 class meetings) before November 5, you will automatically
be dropped from the class and receive a “W.” (This policy will be valid for both excused and unexcused absences
and will hold regardless of your grade up to this date.) After November 5, your grade will be dropped by a full letter

++
(b) If you are a borderline grade (for example: 89.9% = B ), and you have a good attendance record (2 absences
or less), I will round your grade up to the higher grade, for example: A. (note: 89.4% is NOT considered a

(c) If you are tardy (more than 10 minutes late) for two-week’s worth of classes (4 class meetings) before November
5, you will automatically be dropped from the class and receive a “W.” (This policy will be valid for both excused
dropped by a full letter grade.

Course Outline:

Week of:              Tuesday                                             Thursday
1.1 Intro to Systems of Linear Equations,               1.2 Gaussian Elimination and Gauss-Jordan
August 17         The concept of parametrization, The concept of          Elimination (i.e. Using augmented matrices to
triangularization                                       solve systems of linear equations)

Take-Home Quiz 1 due                                    2.1 Operations with Matrices (aka Matrix Algebra)
August 24         1.3 Applications of Systems of Linear Equations         2.2 Properties of Matrix Operations

2.3 The Inverse of a Matrix                             2.4, cont’d.
August 31         2.4 Elementary Matrices                                 2.5 Applications of Matrix Operations:
In-Class Quiz 2                                         Crytography and Leontief Input-Output Models

3.1 The Determinant of a Matrix                         3.2 Evaluation of a Determinant Using Elementary
September 7                                                               Operations
In-Class Quiz 3                                         3.3 Properties of Determinants

3.5 Applications of Determinants
MIDTERM 1                                               (skip 3.4)
September 14

Take-Home Quiz 4 due                                    4.2 Vector Spaces
September 21      4.1 Vectors in ℜ , Vector Addition and                  4.3 Subspaces of Vector Spaces
n

Subtraction, Scalar Multiplication, Magnitude

4.4 Spanning Sets and Linear Independence               4.5 Basis and Dimension
September 28      In-Class Quiz 5
SYLLABUS         MATH 254 Sect. No. 01                 Fall ‘04   Class No. 5341        page 3 of 3

Course Outline, cont’d.

Week of:              Tuesday                                              Thursday
Take-Home Quiz 6 due                                 4.6, cont’d.
October 5        4.6 Rank of a Matrix, Row-Space, Column-Space,       4.7 Coordinates and Change of Bases
Null-Space

4.8 Applications of Vector Spaces: Differential
October 12                                                            Equations and the Wronskian
MIDTERM 2

5.1 Length and Dot Product in ℜ , The Cauchy-        5.2 cont’d. Orthogonal Projections in Inner
n
October 19       Schwarz Inequality, The Triangle Inequality,         Product Spaces
5.2 Inner Product Spaces    In-Class Quiz 7

Take-Home Quiz 8 due                                 5.4 Mathematical Models and Least Squares
October 26       5.3 Orthonormal Bases: The Gram-Schmidt              Analysis
Process

Take-Home Quiz 9 due                                 5.5, cont’d. Fourier Approximations
5.5 Applications of Inner Product Spaces: The
November 2       Cross Product, Least Squares Approximations for
Functions
Take-Home Quiz 10 due                                6.2 The Kernel and Range of a Linear
November 9       6.1 Linear Transformations                           Transformation, Concepts of One-to-One and
Onto, Isomorphisms

6.2, cont’d.
November 16      6.3 Matrices for Linear Transformations
In-Class Quiz 11

6.4 Transition Matrices and Similarity,             HOLIDAY
November 23      Concept of Diagonalization                           No Classes
In class Quiz 12                                     Happy Thanksgiving!

7.1 Eigenvalues and Eigenvectors
November 30      MIDTERM 3                                            7.2 Diagonalization

7.3 Symmetric Matrices and Orthogonal                7.4 Applications of Eigenvalues and Eigenvectors
Diagonalization; The Real Spectral Theorem           Quadratic Forms and Systems of Linear DE’s
December 7

Comprehensive (everything!)
December 14      FINAL EXAM from                                      Happy Winter Break!!!
10:30am -12:00noon in Room 704B

ON-CAMPUS FREE TUTORING: One-on-one, group, and open, walk-in lab assistance is provided
free to all Southwestern College students at the following locations. (Check front door for days and
times.)
Math Lab, Room 393.

MESA (Math, Engineering, Science Achievement Program) Room 323A.

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