Math 471 Course Syllabus (Last updated June 21st)

MATH 471, Summer 2021, June 29 – August 19 (Last day of classes is August 16)

Introduction to Numerical Methods

Instructor: Dao Nguyen (Links to an external site.) (nntdao@umich.edu)

Class Time: Tuesday, Wednesday, Thursday 10:00AM-12:00PM, Ann Arbor time.

Class Location: East Hall B844

All lectures (in person) will be recorded automatically by the University and visible upon request to registered students for this course.

Office Hours (Tentative): Tuesday, Wednesday, Thursday, 1:00 -2:00PM, or by appointment.

Course Piazza site: piazza.com/umich/summer2022/c1b3 (Links to an external site.).

Textbook: There is no required textbook. Instead, lecture notes will be posted on the course website after each class. For supplementary reading, the following options are recommended.
1. “Numerical Computing with Matlab”, by Cleve Moler, SIAM, ISBN: 0-89871-560-1
1a. a copy may be purchased from SIAM
1b. a free copy is available at the MathWorks: www.mathworks.com/moler/chapters.html (Links to an external site.)
2. “A Friendly Introduction to Numerical Analysis”, by Brian Bradie, Prentice Hall, ISBN: 0130130540, there should be inexpensive used copies available in local bookstores or online booksellers
3. “Numerical Methods”, by Germund Dahlquist and Ake Bjork, Dover, ISBN: 0486428079

Prerequisites: The following statement is quoted directly from the course description: “MATH 216, 256, 286, or 316; and 214, 217, 417, or 419; and a working knowledge of one high-level computer language.”

About the Course: This course covers a variety of numerical methods, many of which are still widely used in science and engineering today. (Others are a bit outdated but set the foundations for later/more advanced methods) A numerical method describes a sequence of steps, or an algorithm, for solving a mathematical problem, such as solving a system of equations and looking for the value of an integral or a function, on a machine. In addition to the collection of methods, this course also introduces ideas such as accuracy, e ciency, and stability, which are common measures of how good the methods are. Some of the lectures will contain in-class programming demonstrations in MATLAB so that students can see the methods/algorithms in action and gain a more practical understanding of them.

Course Content:

Finite precision arithmetic, finite-difference approximation of a derivative (Chap 1);
Solving nonlinear equations, root-finding (Chap 2);
Numerical linear algebra, finite-difference schemes for boundary value problems (Chap 3);
Eigenvalues (Chapter 4);
Polynomial and spline interpolation (Chap 5);
Numerical integration (Chap 6);
Time-dependent ordinary and partial differential equations (time permits), Numerical Methods for Differential Equations (Chap 7&8).

Class Website/ Access to Course Materials: All course materials are accessible through the course’s Canvas page. Students should make sure they can receive notifications/announcements from Canvas and check the Canvas course page regularly.

Graded Assignments and Policy: Seven homework will be assigned. They will be posted and submitted to Canvas unless specified otherwise.

Each homework assignment will contain both theoretical and programming questions. Students are strongly encouraged to discuss the problems with their classmates; however, each student must write their own solution and codes. MATLAB is recommended for all programming questions. Students need to cite any resources other than the textbook, course materials, and Matlab’s built-int help documentation and Mathworks documentations. For example, if a pseudo code from Wikipedia is used in solving one of the programming questions, a link to the page should be cited in the homework solution. Similarly, any stack overflow post or other online learning platform pages should be cited as well. Missing such citations may be regarded as an academic integrity violation.
For all homework assignments, students are expected to fully understand their submitted solutions and codes (note: “fully understand” does not mean completely mathematically correct argument or functioning codes; it means the student understands what they submitted). Students may be asked, in a follow-up private zoom meeting, to orally explain their solutions to the instructor after submission, and this may affect the student’s grade.

Exams:

Midterm: July 19th 1:00 – 2:00 PM (accommodations for time conflicts need to be communicated with the instructor by July 14th);
Final: August 18th 1:00 – 2:00 PM ~~(there will not be any accommodations for time conflicts for the final exam).~~

All exams are closed-book exams. For each exam, students can use one piece and both sides of an 8.2 by 11-inch handwritten information sheet. If used, the information sheet needs to be scanned (on both sides) and submitted as part of the exam submission. For all exams, students are expected to fully understand their submitted solutions. Students may be asked to orally explain their solutions to the instructor in a private meeting after the exams as follow-ups, and this may affect the student’s grade.

Grading Policy:

Homework: 45%,
Midterm Exam: 20%,
Final Exam: 35%,

No-grade Assignments: Two surveys will be assigned to collect student information and feedback. These are designed to help facilitate online teaching/learning and thus will not contribute to students’ grades.

Others:

Academic Integrity

According to the LSA Community Standards of Academic Integrity, the College prohibits all forms of academic dishonesty and misconduct. Academic dishonesty may be understood as any action or attempted action that may result in creating an unfair academic advantage for oneself or an unfair academic advantage or disadvantage for any other member or members of the academic community. Conduct, without regard to motive, that violates the academic integrity and ethical standards of the College community cannot be tolerated. Do not cheat. If you cheat in this class, you risk failing the course. If you have any questions about what is, or is not, allowed in this course, please ask.

Accommodations for Students with Disabilities

If you think you need accommodations for a disability, please let your instructor know as soon as possible. A Verified Individualized Services and Accommodations (VISA) form must be provided to your instructor at least two weeks prior to the need for a test/quiz accommodation. The Services for Students with Disabilities (SSD) Office (Links to an external site.) (G664 Haven Hall) issues VISA forms.

Classroom Culture of Care

LSA is committed to delivering our mission while aiming to protect the health and safety of the community, which includes minimizing the spread of COVID-19. Our entire LSA community is responsible for protecting the collective health of all members by being mindful and respectful in carrying out the guidelines laid out in our Wolverine Culture of Care (Links to an external site.) and the University’s Face Covering Policy for COVID-19 (Links to an external site.). Individuals seeking to request an accommodation related to the face-covering requirement under the Americans with Disabilities Act should contact the Office for Institutional Equity (Links to an external site.).

While attending any of the optional face-to-face resources for this class, students are expected to adhere to the required safety measures and guidelines of the State of Michigan and the University of Michigan, including sanitizing their work areas, maintaining 6 feet or more of personal distance, wearing a face-covering that covers the mouth and nose in all public spaces, and not coming to class when ill or in quarantine. This course will also limit the number of persons in attendance at these resources.

Students who do not adhere to these safety measures while attending any of the optional face-to-face resources for this class and who do not have an approved exception or accommodation will be asked to leave.

For additional information refer to the LSA Student Commitment to the Wolverine Culture of Care (Links to an external site.) and the OSCR Addendum to the Statement of Student Rights and Responsibilities on the OSCR website (Links to an external site.).

Class rules: 1. Questions during class are highly encouraged. 2. Be respectful to other people.