### Math 1080: Numerical Linear Algebra

#### Instructor: Catalin Trenchea

Lectures: MWF 11:00-11:50am Thackeray 627

#### Office Hours: M 2:00pm-3:30pm, W 9:00am-10:30am and by appointment

Office: Thackeray 606

Phone: (412) 624-5681

E-mail: trenchea@pitt.edu

**Textbook** *Numerical Mathematics and Computing* fifth
edition, by W. Cheney and D. Kincaid. Available from Pitt Bookstore.
**Content**
This course is an introduction to numerical linear algebra which addresses numerical methods
for solving linear algebraic systems and matrix eigenvalue problems
and applications to partial differential equations. Although the course will stress a computational viewpoint,
analysis of the convergences and stability of the algorithms will be investigated.
We will cover the following chapters in the textbook: systems of linear equations, ordinary differential
equations, least-squares method, boundary value problem, partial differential equations
and minimization of functions.

**Grading Policy** The final grade will be based on
homeworks (40%), and exams (60%).
Late homework will be accepted only by special permission of the
instructor.

#### Homeworks

The printouts of the codes should be included.
Hwk 1 (due 01/19/09): problem 2, 9, 15 pages 292-294; problem 2, 9 page 296
and problem: Count the number of additions in naive Gaussian elimination.
Hwk 2 (due 01/30/09): problem 5 page 307, computer problems 3, 6, 18, and
count the number of additions and multiplications in naive Gaussian elimination of
tridiagonal matrices.
Hwk 3 (due 02/06/09): problem 4, 9, page 332; problem 1, 4 page 336, and two more problems.
Hwk 4 (due 02/13/09): problem 3, 8 page 353; problem 2, 3, 7, 8 page 355.
Hwk 5 (due 02/20/09): problem 12 p 370, problem 1 a,b,c,d p. 371, problem 4 page 381 and one
problem.
Hwk 6 (due 02/27/09): problem 5,6 page 455 and problem 3,5,6 page 457.
Hwk 7 (due 03/13/09): problem 13, 18 page 467, problem 7 (plot the numerical solution), 10 page 469,
problem 5 page 481, problem 5 page 483 and problem 3 page 499.
Hwk 8 (due 03/20/09): problem 3, 19 page 529, problem 3, 4, 9 page 543, problem 22 page 555 and one
problem.
Hwk 9 (due 03/27/09): problem 4, 5, 7 page 610 and problem 2a page 611 using finite difference method
for N=10, 20, 40; and plot the numerical solution and error.
Hwk 10 (due 04/03/09): problem 1a, 1b, 1c, 1d, 3, 5 page 627 and problem 4 page 636.

Midterm in class: March 2, 2009.
Take-home final.

Matlab Tutorial:
ps;
HTML

If you have a disability for which you are or may
be requesting an accomodation, you are encouraged to contact both your
instructor and the Office of Disability Resources and Services, 216
William Pitt Union, (412)648-7890/(412)383-7355 (TTY), as early as
possible in the term. DRS will verify your disability and determine
reasonable accomodations for this course.