Course Syllabus
Course Staff & Schedule
Instructor
Hari Sundar
🏢 2692 WEB ☎ 801-585-6673 ✉ hari@cs.utah.edu
Office hours: Tue 11am-noon, WEB 2692
Lecture
Tu,Th 9:10am-10:30pm, M LI 1130
Course Overview
Our primary goal would be to solve partial differential equations numerically. This course will focus heavily on the math and numerics, but you will be expected to implement the methods we cover in a language of your choice. Good options are high-level languages with strong linear algebra support/libraries such as Matlab, Julia or Python with NumPy/SciPy. Familiarity with at least one of these is strongly recommended.
Prerequisite: Adv. Scientific Computing I or a graduate-level linear algebra course plus good understanding of ordinary differential equations.
Course Organization
Lectures. We will meet for lecture twice a week for 80 minutes. I will use a combination of a laptop and a (digital) whiteboard during lectures. I will use the laptop to present programming examples and perform demonstrations; I also make use of slides. I will make the laptop-based examples available online, but you will need to take notes if you want to keep track of what I write on the board or say out loud.
There is no substitute for attending lectures; I expect all students to attend all lectures. You will not be able to completely reconstruct lectures after the fact from the slides and examples that I post online. There is no substitute for participating actively in lecture; I expect all students to put away their electronic devices and pay attention. You may think you’re good at multi-tasking, but I disagree.
There is no formal textbook for this course. I will post notes on canvas, but please note that this is not a replacement for what we cover in class.
These will be up to 6 homework assignments that are a combination of math and programming problems. The problems are set as practical problems that you will first work the math out for and then implement to solve the problem numerically. All assignments are worth 100 points and your final grade will be determined based on your average score across all assignments. We will not be having any exams in this course.
Cooperation vs. Cheating
Working with others on assignments is a good way to learn the material and we encourage it. However,there are limits to the degree of cooperation that we will permit. When taking an online quiz or an in-class exam, you must work completely independently of everyone else. Any collaboration here, of course, is cheating.
You must limit your discussions with other students of programs or written assignments to a high-level discussion of solution strategies. If you do collaborate with other students in this way, the solution that you submit must identify the students and describe the nature of the collaboration. The solution that you hand in for programs or written assignments must be written in your own words. If you base your solution on any other written solution, regardless of the source, you are cheating.
We do not distinguish between cheaters who copy others’ work and cheaters who allow their work to be copied.
If you have any questions about what constitutes cheating, please ask.
If you cheat, you will be given an E in the course and your case will be handled as detailed here (Links to an external site.).
College of Engineering Policies and Guidelines
For information about adding courses, withdrawing from courses, appealing grades, and more, please refer to the website maintained by the College of Engineering's Office of Academic Affairs.
University of Utah Policies
The Americans with Disabilities Act. The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 801–581–5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.
University Safety Statement. The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801–585–COPS (801–585–2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit safeu.utah.edu (Links to an external site.).
Addressing Sexual Misconduct. Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran's status or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to the Title IX Coordinator in the Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801–581–8365, or the Office of the Dean of Students, 270 Union Building, 801–581–7066. For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801–581–7776. To report to the police, contact the Department of Public Safety, 801–585–2677 (COPS).
COVID-19 Campus Guidelines. Students are required to self-report if they test positive for COVID-19. To report, please contact:
COVID-19 Central @ The U
801–213–2874
coronavirus.utah.edu (Links to an external site.)
Some students may qualify for accommodations and exemptions from these guidelines through the Americans with Disabilities Act (ADA). Accommodations should be obtained prior to the first day of class.
If you believe you meet these criteria, contact:
Center for Disability & Access
801–581–5020
disability.utah.edu (Links to an external site.)
162 Union Building
200 S. Central Campus Dr.
Salt Lake City, UT 84112
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Tentative Course Coverage
- Numerical Methods for Partial Differential Equations (Intro, Fourier Analysis)
- Finite Difference Discretization
- Elliptic Equations
- 1D Problem
- FD Formulas and Multidimensional Problems
- Parabolic Problems
- Elliptic Equations
- Solution Methods
- Iterative Techniques
- Multigrid Techniques
- Direct Solvers
- Hyperbolic Equations
- Finite Difference Discretization of Hyperbolic Equations: Linear Problems
- Scalar One-Dimensional Conservation Laws
- Numerical Schemes for Scalar One-Dimensional Conservation Laws
- Finite Element Methods for Elliptic Problems
- Variational Formulation: The Poisson Problem
- Discretization of the Poisson Problem in R1
- Formulation
- Theory and Implementation
- The Poisson Problem in R2Finite Element Methods for Elliptic Problems
- Integral Equation Methods
- Discretization of Boundary Integral Equations
- Numerical Quadrature
- Discretization Convergence Theory
- Formulating Boundary Integral Equations
- First and Second Kind Potential Equations
Course Summary:
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