MATH 1080: NUMERICAL LINEAR ALGEBRA SPRING 2023
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MATH 1080: NUMERICAL LINEAR ALGEBRA
SPRING 2023
Instructor: Catalin Trenchea, 612 Thackeray Hall, [email protected], www.pitt.edu/˜trenchea Office hours: MW 11:00AM-11:50AM and by appointment.
Lecture: MWF 10:00-10:50, Thackeray 524.
Class web page: www.pitt.edu/˜trenchea/Math1080 −Spring −Semester −2023.html
Textbook: Numerical Mathematics and Computing, fifth edition, by W. Cheney and D. Kincaid. Available from Pitt Bookstore.
Prerequisites: Single variable calculus. Knowledge of linear algebra and differential equations will be useful, but not required.
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 sta- bility 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.
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.
Additional references:
Numerical Mathematics, second edition, by A. Quarteroni, R. Sacco, F. Faleri.
Numerical Methods in Scientific Computing, volume I, by G. Dahlquist, A. Bjorck. SIAM. Numerical Methods, by G. Dahlquist, A. Bjorck. Dover.
Numerical Linear Algebra, by Lloyd N. Trefethen, David Bau, III. SIAM.
Numerical Analysis, by Timothy Sauer. Pearson.
Introduction to linear algebra, fourth edition, by Gilbert Strang. Wellesley Cambridge Press.
Homework assignments: Written homework and several computational projects will be assigned. Late homework will be accepted only by special permission of the instructor. Computer assignments will use Matlab, software by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. An introduction to Matlab will be given at the beginning of the course. A set of matlab codes implementing the numerical algorithms is provided by the authors of the text and is available on the class web page. The computer assignments will utilize this software and will emphasize analyzing the behavior of the algorithms rather than coding them.
The printouts of the codes should be included.
● Hwk 1: problems 2, 9, 15 pages 292-294 (respectively pages 272-275 in the 6th edition, or pages 98-100 in the 7th edition); 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.
● Hwk 2: problem 5 page 307 (respectively page 287 in the 6th edition, or page 110 in the 7th edition), computer problems 3, 6, 18, and count the number of additions and multiplications in naive Gaussian elimination of tridiagonal matrices.
● Hwk 3: problems 4, 9, page 332 (respectively page 311 in the 6th edition, or page 376 in the 7th edition); problems 1, 4 page 336 (respectively page 316 in the 6th edition, or page 378 in the 7th edition), and two more problems.
● Hwk 4: problems 3, 8 page 353 (respectively page 337 in the 6th edition, or page 422 in the 7th edition); computer problems 2, 3, 7, 8 page 423 (respectively page 339 in the 6th edition, or page
311 in the 7th edition).
● Hwk 5: problems 12 page 370 (respectively page 357 in the 6th edition, or page 394 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.
● Hwk 6: problems 5,6 page 455 (respectively page 436 in the 6th edition, or page 309 in the 7th edition), and computer problems 3,5,6 page 457 (respectively page 438 in the 6th edition, or page
310 in the 7th edition).
● Hwk 7: problems 13, 18 pages 466-467 (respectively page 446 in the 6th edition, or page 317 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).
● Hwk 8: problems 3, 19 page 529 (respectively pages 502-504 in the 6th edition, or page 433 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.
● Hwk 9: problems 4, 5, 7 page 610 (respectively pages 578-579 in the 6th edition, or page 521 in the 7th edition), and 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.
● Hwk 10 (due 04/03/20): problems 1a, 1b, 1c, 1d, 3, 5 page 627 (respectively page 594 in the 6th edition, or page 535 in the 7th edition), and problem 4 page 636 (respectively page 604 in the 6th edition, or page 543 in the 7th edition).
Midterm in class: March 2, 2023. Take-home final.
University of Pittsburgh offers many academic skills workshops.
Disability Resource Services
If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.
Academic Integrity
Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pittsburgh Policy on Academic Integrity will incur a minimum sanction of a zero score for the quiz, exam or paper in question. Additional sanctions may be imposed, depending on the severity of the infraction. On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.
Statement on Classroom Recording
To address the issue of students recording a lecture or class session, the University’s Senate Educational Policy Committee issued the recommended statement on May 4, 2010. ”To ensure the free and open discus- sion of ideas, students may not record classroom lectures, discussion and/or activities without the advance written permission of the instructor, and any such recording properly approved in advance can be used solely for the student’s own private use.”
2023-01-28