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 (pp. 272 in the 6th ed.); problem 2, 9 page 296 (pp. 276 in the 6th ed.) and problem: Count the number of additions in naive Gaussian elimination.
  • Hwk 2 (due 01/30/09): problem 5 page 307 (pp. 287 in the 6th ed.), 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 (pp. 311 in the 6th ed.); problem 1, 4 page 336 (Computer problems 8.1, page 316), and two more problems.
  • Hwk 4 (due 02/13/09): problem 3, 8 page 353 (pp. 237 in the 6th ed.); problem 2, 3, 7, 8 page 355 (pp. 339 in the 6th ed.).
  • Hwk 5 (due 02/20/09): problem 12 p 370 (pp. 357 in the 6th ed.), problem 1 a,b,c,d p. 371 (pp. 358 in the 6th ed.), problem 4 page 381 (pp. 369 in the 6th ed.) and one problem.
  • Hwk 6 (due 02/27/09): problem 5,6 page 455 (pp. 436 in the 6th ed.) and problem 3,5,6 page 457 (pp. 438 in the 6th ed.).
  • Hwk 7 (due 03/16/09): problem 13, 18 page 467 (pp. 446 in the 6th ed.), problem 7 (plot the numerical solution), 10 page 469 (pp. 448 in the 6th ed.), problem 5 page 481 (pp. 460 in the 6th ed.), problem 5 page 483 (pp. 462 in the 6th ed.) and problem 3 page 499 (pp. 475 in the 6th ed.).
  • Hwk 8 (due 03/20/09): problem 3, 19 page 529 (pp. 502 in the 6th ed.), problem 3, 4, 9 page 543 (pp. 516 in the 6th ed.), problem 22 page 555 (pp. 529 in the 6th ed.) and one problem.
  • Hwk 9 (due 03/27/09): problem 4, 5, 7 page 610 (pp. 578 in the 6th ed.) and problem 2a page 611 (pp. 580 in the 6th ed.) 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 (pp. 594 in the 6th ed.) and problem 4 page 636 (pp. 604 in the 6th ed.).
    Midterm in class: March 2, 2009.

    Take-home final.

  • Matlab Tutorial: ps; HTML

    • Software

  • A collection of matlab codes accompanying the text
    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.