.. _info: ============================================================= Course information ============================================================= Instructor --------------- * `Prof. Randall LeVeque `_ * Office: Lewis 328 * netid for email: rjl * Office hours in Lewis 328: Monday 11:00am-12:00pm and Tuesday 4:00-5:00pm * Office hours online: Monday 5:00-6:00pm and Tuesday 7:00-8:00am (Pacific) (see `Canvas `_ for connection information) TA --------------- * `Scott Moe `_ * netid for email: smoe * Office hours in Lewis 128: Monday 4:30-5:30pm and Friday 11:00am-12:00pm * Office hours online: Monday 12:00-1:00pm and Friday 5:00-6:00pm (Pacific) (see `Canvas `_ for connection information) Lectures --------- * MWF 2:30 - 3:20 pm in Loew 216 Canvas Page ----------- Registered students should have access to the `Canvas course page `_, where you will find links to videos of lectures, the discussion board, and additional information about homeworks and exams. Assignments ----------- See :ref:`homeworks` for more information and due dates. Course Description ------------------ This course is an introductory graduate level course in numerical methods designed to give engineering, mathematics, and science students the expertise necessary to understand and use computational methods for solving scientific problems. The emphasis is on methods for linear algebra problems (direct methods for linear systems, linear least squares problems, and algebraic eigenvalue problems). This course is the first in a series of three numerical methods courses. Amath 585 treats boundary value problems (ODEs and PDEs) and iterative methods for their numerical solution. Amath 586 treats initial value problems (ODEs), parabolic and hyperbolic PDEs and methods for their numerical solution. This is a five (5) credit course. Prerequisites ------------------ * Some Computing Programming (Matlab, Python, R, Fortran, or C) * Linear Algebra (e.g. MATH 308, AMATH 352, or equivalent) Computer Software ------------------ Please use either Matlab or Python. Examples will be presented in both languages in some cases. See :ref:`software` for more about your options. Textbook -------- * Lloyd N. Trefethen and David Bau, III, `Numerical Linear Algebra `_, SIAM, 1997, ISBN-13: 978-0-898713-61-9. Note that you can purchase it direct from `SIAM `_ with a substantial discount if you are a SIAM member, and that `student membership `_ is free! See :ref:`biblio` for some other resources you might find useful. Topics to be covered -------------------- We will cover much of parts I through V of Trefethen and Bau, `Numerical Linear Algebra `_, along with some supplementary material. In particular: * Review of basic linear algebra in finite dimensional spaces, including both :math:`R^n` and also function spaces. * Linear independence, bases, norms, matrix factorization, etc. * Orthogonality and the Singular Value Decomposition (SVD). * Least squares problems: QR factorizations, Gram-Schmidt, Householder transformations. * Conditioning of problems and stability of algorithms. * Linear systems of equations: Gaussian elimination and LU factorizations. * The eigenvalue problem: the power method and QR algorithms, relation to SVD. * Various applications of the above algorithms will also be considered. Grading ------- Homework: 50%, midterm exam: 25%, final exam: 25%. There will be 5 homework assignments. See :ref:`homeworks` for more information and due dates.