Lectures : MWF 10:00-10:50AM Thackeray 524

Office: Thackeray 606

Phone: (412) 624-5681

E-mail: trenchea@pitt.edu

**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.

This course fulfills the requirements for the following Math majors: The Bachelor of Science in Mathematics, The Bachelor of Science in Applied Mathematics, The Bachelor of Science in Actuarial Mathematics, and The Bachelor of Science in Mathematical Biology, offered by the Department of Mathematics.

problems: 2, 9 page 296 (respectively page 276 in the 6th edition, or pages 100-101 in the 7th edition), and

problem: Count the number of additions in naive Gaussian elimination.

computer problems 3, 6, 18, and

count the number of additions and multiplications in naive Gaussian elimination of tridiagonal matrices.

problems 1, 4 page 336 (respectively page 316 in the 6th edition, or page 378 in the 7th edition), and two more

problems. Extra credit: exercise 22 , page 336 (respectively 315 in the sixth edition).

computer problems 2, 3, 7, 8 page 355 (respectively page 339 in the 6th edition, or page 311 in the 7th edition).

computer problem 1 a,b,c,d page 371 (respectively pages 358 in the 6th edition, or page 395 in the 7th edition),

computer problem 4 page 381 (respectively page 369 in the 6th edition, or page 404 in the 7th edition), and one

problem.

computer problems 3,5,6 page 457 (respectively page 438 in the 6th edition, or page 310 in the 7th edition).

computer problem 7 (plot the numerical solution), 10 page 468 (respectively page 448 in the 6th edition,or page 318 in the 7th edition),

problem 5 page 481 (respectively page 460 in the 6th edition, or page 329 in the 7th edition),

computer problem 5 page 483 (respectively page 462 in the 6th edition, or page 329 in the 7th edition), and

computer problem 3 page 499 (respectively page 475 in the 6th edition, or page 346 in the 7th edition).

problems 3, 4, 9 page 543, problem 22 page 555 (respectively page 529 in the 6th edition, or page 446 in the 7th edition)

and one problem.

computer problem 2a page 611 (respectively page 580 in the 6th edition, or page 522 in the 7th edition) using finite difference method for N=10, 20, 40; and plot the numerical solution and error.

problem 4 page 636 (respectively page 604 in the 6th edition, or page 543 in the 7th edition).

Midterm in class: March 2, 2020.

Take-home final.