Instructor: Prof. Hans De Sterck, office: MC5016, email: hdesterck@uwaterloo.ca
Lectures: 2:30-3:20MWF (MC 2035)
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:
Mathematical models based on partial differential equations (PDEs) are ubiquitous these days, arising in all areas of science and engineering, and also in finance and economics. In complex models, the PDEs cannot be solved exactly, and one has to rely on approximate solutions obtained using numerical methods on computers.
The goal of this course is twofold. You will receive a solid introduction to the theory of numerical methods for partial differential equations (with derivations of the methods and some proofs). You will learn to implement the computational methods efficiently in Matlab, with some applications to problems in several fields, including heat transfer, wave phenomena and fluid mechanics.
Prerequisites: (AMATH 341/CM 271/CS 371 or CS 370) and (AMATH 350 or AMATH 351 or AMATH 342/CM 352). You will also be able to enroll in the course through consent of the instructor if you have credit in AMATH 353 (PDE 1).
Tentative Outline:
I. Overview of PDEs (2 weeks)
II. Finite Difference (FD) Methods (4 weeks)
III. Finite Volume (FV) Methods (3 weeks)
IV. Finite Element Methods (FEM) (3 weeks)
Course Material: A full set of course notes is available for download at http://www.math.uwaterloo.ca/~hdesterc/websiteW/teaching/AM442CM452.pdf, or for purchase in Pixel Planet/MC2018.
Course Website: the ACE system will be used extensively for all course communications.
Reference Material:
Books on reserve in library:
1. A first course in the numerical analysis of differential equations, Iserles, Cambridge University Press, 1997. (FD and FEM, Chapters 7-14) (on 1-day reserve in Davis library)
2. Finite volume methods for hyperbolic problems, Leveque, Cambridge, 2002. (FV) (on 1-day reserve in Davis library)
3. An introduction to the finite element method, Reddy, McGraw-Hill, 1993. (FEM, comprehensive introduction with engineering applications) (on 1-day reserve in Davis library)
4. The mathematical theory of finite element methods, Brenner and Scott, Springer, 1994. (FEM, theoretical) (on 1-day reserve in Davis library)
5. Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, Leveque, SIAM, 2007. (FD)(on 1-day reserve in Davis library)
Online resources:
6. Numerical Methods for Partial Differential Equations, MIT Open Course Ware project. (FD, FV and FEM) (download course notes pdf from http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/16-920JNumerical-Methods-for-Partial-Differential-EquationsSpring2003/LectureNotes/index.htm)
7. Finite difference methods for differential equations, Leveque. (FD) (download course notes pdf from http://www.amath.washington.edu/~rjl/pubs/am58X/amath58X05.pdf)
8. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Trefethen. (FD) (download course notes pdf from http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html)
Reference material on PDEs:
9. Partial differential equations I, Wainwright and Siegel, Course Notes for AMATH 353 (good general background resource for PDEs; available in Pixel Planet/MC2018, and on 1-day reserve in Davis library)
Assignments: There will be three Computational Assignments (21% weight in final grade, programming in Matlab), and three smaller Theoretical Assignments (9% weight in final grade). Assignments will generally be due on Mondays, 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): |
|
Theoretical 1 |
Sep 21 |
Sep 28 |
|
Computational 1 |
Sep 28 |
Oct 14 |
|
Theoretical 2 |
Oct 14 |
Oct 23 |
|
Computational 2 |
Nov 2 |
Nov 16 |
|
Theoretical 3 |
Nov 16 |
Nov 23 |
|
Computational 3 |
Nov 23 |
Dec 4 |
Final Grade: 20% Midterm Exam, 50% Final Exam, 9% Theoretical Assignments (3), 21% Computational Assignments (3). (The midterm and final exams will be closed-book exams, but you will receive an extensive formula sheet. The midterm exam is planned for Thursday October 29, afternoon/evening.)
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 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 ÒrulesÓ for group work/collaboration should seek guidance from the course instructor, academic advisor, or the undergraduate 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 departmentÕs 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.