CM 770: Numerical Analysis
Instructor: Prof. Hans De Sterck, office: MC5016, email: hdesterck@uwaterloo.ca
Lectures: 10:30-11:50WF (RCH 212)
Office hours: 4:00-5:00M and 4:00-5:00Thu (MC5016)
TA: Killian Miller, office: MC6091h, email: killian.miller@gmail.com
Office hours: 1:00-2:00Tue and 1:00-2:00W (MC6091h)
Course Description and Objectives:
The goal of this course is twofold. You will receive a solid introduction to the theory of several important classes of numerical methods (with derivations of the methods and some proofs), and you will learn to implement the numerical methods efficiently in Matlab, with some applications to problems in several fields.
This is a core course in the Computational Mathematics MasterŐs program, providing base knowledge in the numerical methods that are employed in further courses in this program. This course can also be taken as a solid introductory course on numerical methods by graduate students from other programs in Mathematics, Science and Engineering. In particular, CM 770 may be a good preparation for AM 741/CS 778: Numerical Solution of Partial Differential Equations, for students without much previous experience in numerical methods.
Prerequisites: A basic undergraduate course on numerical methods, as well as some experience in Matlab programming, are strongly recommended. Students who have previously taken two or more courses on numerical methods, including a course on numerical linear algebra, are not recommended to take this course.
Tentative Outline:
Required textbook: Introduction To Numerical Computation, by Elden, Wittmeyer-Koch, and Nielsen, Studentlitteratur AB, 2004 (available from UW Bookstore).
Other references:
á Numerical linear algebra, by Trefethen and Bau, SIAM, 1997 (on 1-day reserve in the Davis library)
á A Multigrid Tutorial, by Briggs, Henson and McCormick, SIAM, 2000 (on 1-day reserve in the Davis library)
á Iterative methods for sparse linear systems (2nd edition), Yousef Saad, SIAM, 2003 (on 1-day reserve in the Davis library)
á Iterative methods for sparse linear systems (1st edition), Yousef Saad, available online from
www-users.cs.umn.edu/~saad/books.html
Course Website: the ACE system will be used extensively for all course communications.
Assignments: There will be approximately six assignments, with a mix of theoretical questions and programming questions. Assignments will generally be due on Fridays, at the beginning of class. Marked assignments will be given back in class. Some problems may not be marked (solutions will be provided for these problems). Late submissions will not be graded, except under special circumstances (discuss with the instructor before the assignment is due).
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Assignments: |
Handout date (tentative): |
Due date (tentative): |
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Assignment 1 (floating point) |
Sep 18 |
Sep 25 |
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Assignment 2 (rootfinding) |
Sep 25 |
Oct 9 |
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Assignment 3 (ODE) |
Oct 9 |
Oct 23 |
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Assignment 4 (LU/QR) |
Oct 23 |
Nov 6 |
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Assignment 5 (iterative/MG) |
Nov 6 |
Nov 25 |
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Assignment 6 (Krylov) |
Nov 25 |
Dec 4 |
Final Grade: 40% Assignments, 60% Final Exam.
(The final exam will be a closed-book exam, but you will be allowed to bring one sheet of paper on which you can write formulas (two-sided).)
Academic Integrity: You are allowed to discuss theoretical and computational assignment problems and your solution strategies with your classmates, and you are allowed to consult external material (for example, reference books and online sources), but you are not allowed to copy any material from a classmate or from an external source for your assignments: all assignment material that you submit (including written documents, program code and graphical output) should be strictly your own work. Compliance will be actively monitored.
More generally, in order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility. [Check www.uwaterloo.ca/academicintegrity/ for more information.]
Discipline: A student is expected to know what constitutes academic integrity [check www.uwaterloo.ca/academicintegrity/] to avoid committing an academic offence, and to take responsibility for his/her actions. A student who is unsure whether an action constitutes an offence, or who needs help in learning how to avoid offences (e.g., plagiarism, cheating) or about ŇrulesÓ for group work/collaboration should seek guidance from the course instructor, academic advisor, or the graduate Associate Dean. For information on categories of offences and types of penalties, students should refer to Policy 71, Student Discipline, www.adm.uwaterloo.ca/infosec/Policies/policy71.htm. For typical penalties check Guidelines for the Assessment of Penalties, www.adm.uwaterloo.ca/infosec/guidelines/penaltyguidelines.htm.
Appeals: A decision made or penalty imposed under Policy 70 (Student Petitions and Grievances) (other than a petition) or Policy 71 (Student Discipline) may be appealed if there is a ground. A student who believes he/she has a ground for an appeal should refer to Policy 72 (Student Appeals) www.adm.uwaterloo.ca/infosec/Policies/policy72.htm.
Grievance: A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70, Student Petitions and Grievances, Section 4, www.adm.uwaterloo.ca/infosec/Policies/policy70.htm. When in doubt please be certain to contact the departmentŐs administrative assistant who will provide further assistance.
Note for Students with Disabilities: The Office for persons with Disabilities (OPD), located in Needles Hall, Room 1132, collaborates with all academic departments to arrange appropriate accommodations for students with disabilities without compromising the academic integrity of the curriculum. If you require academic accommodations to lessen the impact of your disability, please register with the OPD at the beginning of each academic term.
First lecture: Wednesday September 16, 10:30-11:50 (RCH 212).