MATH 1080: Numerical Linear Algebra

Lectures : MW 3:00-4:15PM 704 Thackeray Hall

Office Hours
MW 2:00-3:00PM, and by appointment (also via zoom)
Office: 612 Thackeray Hall
E-mail: trenchea@pitt.edu

Textbook Numerical Mathematics and Computing fifth edition, by W. Cheney and D. Kincaid. Available from Pitt Bookstore. Book's Programs

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.

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. Book's Programs
  • 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

    The printouts of the codes should be included.
  • Hwk 1 (due 01/22/24): 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 (due 02/5/24): 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 (due 02/12/24): problems 4, 9, page 332 (respectively page 311 in the 6th edition, or page 376 in the 7th edition);
      problems 1 (the pseudo-algorithms in Exercise 8.1.14 have typos, see the class' notes), 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).
  • Hwk 4 (due 02/19/24): 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 355 (respectively page 339 in the 6th edition, or page 311 in the 7th edition).
  • Hwk 5 (due 02/26/24): 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 (due 03/04/24): 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 (due 03/18/24): 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 (due 03/25/24): 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 (due 04/01/24): 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 04/08/24): 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: February 26, 2024.

    Take-home final.

  • Matlab Tutorial: ps; HTML
  • Matlab online access.

    • The Department of Mathematics provides opportunities to engage in research, scholarship, and creative experiences.

    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 (DRS), 140 William Pitt Union, 412-648-7890, drsrecep@pitt.edu, (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

    Academic Integrity

    The University of Pittsburgh Academic Integrity Code is available at https://www.provost.pitt.edu/faculty/academic-integrity-freedom/academic-integrity-guidelines. The code states that "A student has an obligation to exhibit honesty and to respect the ethical standards of the academy in carrying out his or her academic assignments." The website lists examples of actions that violate this code. Students are expected to adhere to the Academic Integrity Code, and violations of the code will be dealt with seriously.

    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.

    This is especially notable during this period. 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.
    Please note, in particular, that Pitt has a data sharing arrangement with Chegg.com that enables us to identify in- stances in which Chegg.com has been used to cheat on assessments. Consequences of being caught in this academic integrity violation have included zero scores on assessments and F grades for the course.

    Diversity and Inclusion

    The University of Pittsburgh does not tolerate any form of discrimination, harassment, or retaliation based on disability, race, color, religion, national origin, ancestry, genetic information, marital status, familial status, sex, age, sexual orientation, veteran status or gender identity or other factors as stated in the University's Title IX policy. The University is committed to taking prompt action to end a hostile environment that interferes with the University's mission. For more information about policies, procedures, and practices, see: https://www.diversity.pitt.edu/civil-rights-title-ix-compliance/policies-procedures-and-practices.

    Classroom Recording

    To ensure the free and open discussion of ideas, students may not record classroom lectures, discussion and/or activities not already recorded by the instructor, 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.

    Lectures could be recorded by the instructor, and this may include student participation. Students are not required to participate in the recorded conversation. The recorded lecture may be used by the faculty member and the registered students only for internal class purposes and only during the term in which the course is being offered. Recorded lectures will be uploaded and shared with students through Canvas.

    Copyright

    Some of the materials in this course may be protected by copyright. United States copyright law, 17 USC section 101, et seq., in addition to University policy and procedures, prohibit unauthorized duplication or retransmission of course materials. See the Library of Congress Copyright Office and the University Copyright Policy.