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{\centerline{\bf NUMERICAL METHODS AND LINEAR ALGEBRA }}
{\centerline{\bf Math 2890 Syllabus Spring 2008}}


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\noindent {\bf Space-Time:}  UH 4440 MWF 9-9:50am\par\smallskip

\noindent {\bf Instructor:} Mao-Pei Tsui

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{\bf Office Hours:} UH2080B M 10:00-11:00am, W 2:00-4:00pm, F
10:00-11:00am


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{\bf Phone:} 419-530-2998 {\bf Fax:} 419-530-4720

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{\bf Email:} Mao-Pei.Tsui@Utoledo.edu

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{\bf Homepage:} http://www.math.utoledo.edu/$\sim$mtsui/

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{\bf Class Web Site:}
http://www.math.utoledo.edu/$\sim$mtsui/2890sp08/2890.html


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{\bf Text:} {\it David C. Lay, Linear Algebras and its Applications, third edition SBN-10: 0201709708 }

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{\bf Prerequisites:} MATH 1830, 1850 or 1920

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{\bf Homework:}  Typically, homework will be assigned weekly and
collected at the beginning of the class on the due date. Assignments
and their due dates will be posted on this course website. Late
assignments will not be accepted unless in extraordinary
circumstances. Your solutions must be neat and show all work. If you
do not show your work then you will not receive credit for your
solution. I will drop your two lowest homework scores.

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{\bf Quizzes:}
Throughout the semester, there will be several 15 minute quizzes
given during class, the dates to be announced in advance. The
material in the quizzes will be drawn from the homework and
suggested problems selected for the previous week. The lowest quiz
score will be dropped.




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{\bf Exams:}We will have two in-class one hour midterm exams, and a
two hour final exam.

$\bullet$ Midterm I Feb. 11 (Monday)

$\bullet$ Midterm II Mar. 24 (Monday)

$\bullet$ Final Exam April 29(Tuesday), 10:15-12:15

 The final exam is comprehensive and will slightly place
more emphasis on the material covered after the last in-class exam.



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{\bf Missed Quizzes and Exams:} Absences for quizzes and exams can only be excused if covered by the University's
missed class policy. The policy specifically mentions absences from class may be excused for personal emergencies,
religious observances, participation in certain UT sponsored activities, and government required activities. For
more information see http://www.utoledo.edu/index.asp?id=529. Arrangements for make up quizzes and exams will only
be made if you inform me of the absence without delay by phone or email and present a documented excuse.

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{\bf Grading:} The following percentages are assigned to the
components of the student's grade.

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\halign{\qquad#\hfill&\qquad#\hfill&\qquad#\hfill\cr
Quizzes&10\%&\cr Hand in homework &15\%& \cr Exam I&20\%& \cr Exam
II&20\%\cr Final Exam&35\%&  \cr }

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In computing the quiz grade the lowest quiz score will be dropped.


Your final grade will be determined from the distribution of total
points earned, on the following scale: 90-100\% earns an A; 80-–89\%
earns a B; 70–-79\% earns a C; 60–-69\% earns a D.
 The IW grade will be given to only those
students who have stopped attending class before or on March 24.  If
you have any question about your grade at any time please speak with
me.

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{\bf Resources:} There are resources available for students who need
extra help outside of my office hours. For this courses the most
reliable source of tutorial help can be found at the Mathematics
Learning and Resource Center located in the basement of Carlson
Library(adjacent computer lab).

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{\bf Goals:}

At the end of the course, students should be able to

$\bullet$ make calculations with agility, accuracy, intelligence and
flexibility

 $\bullet$ explain the basic concepts clearly and reason logically
with them.

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{\bf Expectations :}

To achieve these goals, students are expected to

$\bullet$ read each section of the textbook before the material is
presented in class

$\bullet$ attend the lectures

 $\bullet$ complete all homework assignments

  $\bullet$ discuss mathematics with other students and the
  instructor

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{\bf Calendar:} \halign{\qquad#\hfill&\qquad#\hfill \cr Martin
Luther King Day & January 21 \cr Last date to drop & January 22\cr
Exam I & Feb. 11 (Monday)\cr Spring Break & Mar. 3 - Mar. 7
\cr Last date to withdraw & Mar. 21 (Friday)
\cr Exam
II & Mar. 24 (Monday)\cr
Final exam & April 29(Tuesday), 10:15-12:15 \cr}

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\noindent $\hbox{\bf Course outline}$:      This is a course in
numerical methods in linear algebra. The focus of the course is on
matrix factorizations and the algorithms used to find them. The use
of the computer program Matlab is an integrated part of this course.
This is brief outline of the sections covered from the textbook:

$\bullet$       Chapter 1, sections 1.1-1.5, 1.7, 1.8:  linear
systems, row reductions, vector equation, matrix equations, solution
sets, linear independence, linear transformations

$\bullet$      Chapter 2, sections 2.1-2.5, 2.8, 2.9: matrix
operation, matrix inverse, invertible matrices, partitioned
matrices, matrix factorization, subspaces of $R^n$, dimension and
rank;

$\bullet$      Chapter 5, sections 5.1-5.3, 5.8:  eigenvectors,
eigenvalues, characteristic equation, diagonalization, iterative
methods;

$\bullet$      Chapter 6, sections 6.1-6.5:  inner products,
orthogonal sets, orthogonal projections, Gram-Schmidt
orthogonalization process, the method of least squares;

$\bullet$     Chapter 7, sections 7.1-7.2, 7.4:  diagonalization of
symmetric matrices, quadratic forms, singular value decomposition


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