M340L MATRICES AND MATRIX CALCULATIONS,
UNIQUE NUMBER #56185, SPRING 2011
The Course Organization and Requirements
Instructor: Prof. Natasa Pavlovic
Office: RLM 12.162
Phone: 471-1187
E-mail: [email protected]
Office hours: Tue & Thu 11:00 am - noon
Teaching Assistant: Ligang Long
Office: RLM 12.124
Phone: 475-8685
E-mail: [email protected]
Office hours: Mon & Wed 3:00 pm - 5:00 pm
Meeting: Tue & Thu 12:30 pm - 1:45 pm, WAG 101
Course Web Page: Log in at blackboard https://courses.utexas.edu/webapps/portal/frameset.jsp
and choose M340L course, unique number #56185. Check this site regularly for homework problems,
updates, special announcements, etc.
Textbook: Linear Algebra and Its Applications, 3rd edition, by David C. Lay
Course Content: M340L focuses on basic techniques of linear algebra with an emphasis on calculational tools. One of the beautiful features of the subject lies in its applications to numerous
fields including, but not limited to, economy, electrical engineering, biology, physics. Some of these
applications will be illustrated throughout the semester.
We will cover parts of every chapter of the book, as the time permits. For details see a tentative
lecture calendar.
Prerequisites: M408C, M408K, or M408N with a grade of at least C-, or consent of instructor.
Note that credit cannot be received for both M340L and M341.
Calculators: No calculators will be allowed on any of the exams.
Requirements:
(1) Homework:
(a) A problem set will be assigned on (almost) every Thursday (posted at the blackboard
under “Assignments”). It will be collected at the beginning of the class following
Thursday. The first homework assignment will be collected on January 27.
(b) You are encouraged to discuss the homework with fellow students. But what is important
is that each of you write up the assignments on your own, formulating the mathematics
in your words. Staple all pages together, write clearly in complete sentences and please
write your name on your paper.
(c) NO LATE HOMEWORK WILL BE ACCEPTED! Note that 2 lowest scores will be
dropped.
(d) Only a portion of each homework assignment will be fully graded.
(e) You are supposed to pick up your graded homework directly from the TA during his
office hours.
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M340L MATRICES AND MATRIX CALCULATIONS, UNIQUE NUMBER #56185, SPRING 2011
(f) Homework grades will be posted at the blackboard. It is your responsibility to check
that each homework score posted at the blackboard matches your actual score. In case
of a discrepancy, please notify the teaching assistant. Corrections can be made NO
LATER THAN 4 WEEKS after the date when the homework was collected.
(2) Class tests:
• Test 1 on Thursday, February 24 covering sections 1.1 - 1.9, 2.1 - 2.3 and 2.7
• Test 2 on Thursday, April 7 covering sections 3.1 - 3.3, 4.1 - 4.6, 5.1 - 5.3.
Note NO MAKE UP TESTS WILL BE OFFERED.
(3) Final: A comprehensive final exam will be given during finals week as scheduled by the
University in the course schedule (a tentative day: Saturday, May 14, from 2:00 pm - 5:00
pm). Please mark this day in your calendar and plan to be present at the final exam. It is
implicit in your registration for this class that, barring some unforeseen calamity, you affirm
to be present to take the final examination at this time.
Grading: Grades of the requirements will be scaled to count as follows:
• Homework: the lowest 2 scores will be dropped and the rest will count as 25 points
• Class Test 1: 25 points
• Class Test 2: 25 points
• Final Exam: 50 points
The course grade will be determined out of 100 points by dropping the lowest class test, or by
weighting the final exam by 1/2 (i.e. count it as 25 points). The course letter grade will be assigned
according to the following scale:
A 90 - 100
A- 88 - 89.99
B+ 86 - 87.99
B 80 - 85.99
B- 78 - 79.99
C+ 76 - 77.99
C 70 - 75.99
C- 65 - 69.99
D+ 60 - 64.99
D 55 - 59.99
D- 50 - 54.99
F 0 - 49.99
If necessary, the scale is subject to change, but only in students’ favor.
Honor code: The class will be governed by the University of Texas at Austin Honor Code: “The core
values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual
opportunity, and responsibility. Each member of the University is expected to uphold these values
through integrity, honesty, trust, fairness, and respect towards peers and community.”
Students with disabilities: The University of Texas at Austin provides upon request appropriate
academic accommodations for qualified students with disabilities. For more information, contact the
Office of the Dean of Students at 471-6259, 471-6441 TTY.
Religious Holidays: The University of Texas at Austin provides upon request appropriate academic accommodations for religious holidays.
Emergency Classroom Evacuation: Occupants of buildings on The University of Texas at Austin
campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or
announcement requires exiting and assembling outside. Familiarize yourself with all exit doors of
each classroom and building you may occupy. Remember that the nearest exit door may not be the
one you used when entering the building. Do not re-enter a building unless given instructions by the
Austin Fire Department, the University Police Department, or the Fire Prevention Services office.
M340L MATRICES AND MATRIX CALCULATIONS,
UNIQUE NUMBER #56185, SPRING 2011
A tentative1 lecture calendar
Week 1: 1/18, 1/20
1.1 Systems of linear equations
1.2 Row reduction and echelon forms
Week 2: 1/25, 1/27
1.3 Vector equations
1.4 The matrix equation Ax = b
1.5 Solution sets of linear systems
Week 3: 2/1, 2/3
1.6 Applications of linear systems
1.7 Linear independence
Week 4: 2/8, 2/10
1.8 Introduction to linear transformations
1.9 The matrix of a linear transformation
2.1 Matrix operations
Week 5: 2/15, 2/17
2.2 The inverse of a matrix
2.3 Characterization of invertible matrices
2.7 Applications to computer graphics
Week 6: 2/22, 2/24
Review of sections 1.1 - 1.9, 2.1 - 2.3 and 2.7
In-class Test 1 on Thursday, February 24
Week 7: 3/1, 3/3
3.1 Introduction to determinants
3.2 Properties of determinants
3.3 Cramer’s rule, volume, and linear transformations
Week 8: 3/8, 3/10
4.1 Vector spaces and subspaces
4.2 Null spaces, column spaces, and linear transformations
4.3 Linearly independents sets; bases
1The schedule is tentative and it may be accelerated or slowed down. Changes in exam dates are not anticipated.
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M340L MATRICES AND MATRIX CALCULATIONS, UNIQUE NUMBER #56185, SPRING 2011
Week 9: 3/15, 3/17
Spring Break
Week 10: 3/22, 3/24
4.4 Coordinate systems
4.5 The dimension of a vector space
4.6 Rank
Week 11: 3/29, 3/31
5.1 Eigenvectors and eigenvalues
5.2 The characteristic equation
5.3 Diagonalization
Week 12: 4/5, 4/7
Review of sections 3.1 - 3.3, 4.1 - 4.6, 5.1 - 5.3
In-class Test 2 on Thursday, April 7
Week 13: 4/12, 4/14
5.5 Complex eigenvalues
5.6 Discrete dynamical systems
Week 14: 4/19, 4/21
6.1 Inner product, length, and orthogonality
6.2 Orthogonal sets
6.3 Orthogonal projections
Week 15: 4/26, 4/28
6.4 The Gram-Schmidt process
6.5 Least-squares problems
Week 16: 5/3, 5/5
7.1 Diagonalization of symmetric matrices
7.2 Quadratic forms
A comprehensive final exam will be given during finals week as scheduled by the University in
the course schedule (a tentative day: Saturday, May 14, from 2:00 pm - 5:00 pm).