Numerical Methods for Partial Differential Equations
Math 175/275 --- Spring 2021

Under construction.

Lecture site: Remote. Videos are made available on Canvas.
Discussion sessions 175 A01 43577: Thursday 5:00pm-5:50pm, remote
275 A01 43668: Thursday 5:00pm-5:50pm, remote
Meeting ID: 929 6367 9144
Final Exam
time and place
Remotely, June 10th, 2021, 11:30am-2:29pm
Instructor Martin Licht
Email: mlicht AT ucsd DOT edu
Office Hours: Monday, Wednesday, Friday, 5:00pm-5:50pm
Office Hour Meeting ID: 929 6367 9144
Section(s) 43577, 43668
Credit Hours: 4 units
Course content Mathematical background for working with partial differential equations. Survey of finite difference, finite element, and other numerical methods for the solution of elliptic, parabolic, and hyperbolic partial differential equations. (Formerly MATH 172; students may not receive credit for MATH 175/275 and MATH 172.) Graduate students will do an extra paper, project, or presentation, per instructor.
Formal prerequesite MATH 174 or MATH 274, or consent of instructor.
Required textbook The textbook is PDEs with Numerical Methods, by Stig Larsson and Vidar Thomee. (Springer Texts in Applied Mathematics, Volume 45, ISBN 978-3-540-01772-1, hardcover, and 978-3-540-88705-8, softcover) Electronic Version
Homework information Homework is due Sunday 11:59pm and submitted to Gradescope. The entry code for Gradescope is: X3EV68
Final exam Final exam: June 10
Details of the final exam to be announced.
Academic Integrity Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://www-senate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship.
Resources The textbook for this lecture is:
  • Stig Larsson and Vidar Thomee: Partial Differential Equations with Numerical Methods.
    ISBN-13 978-3-540-01772-1
    Electronic Version
The following textbook is recommend to supplement the lecture in regard to background in real and functional analysis: The following textbooks are recommended to supplement the lectures in regard to numerical analysis: Some information about floating point arithmetics:
  • D. Goldberg, What every computer scientist should know about Floating-Point arithmetics. [Link]
  • Information about Floating-Point numbers. [Link]
  • E. Wallace Floating-Point Toy. [Link]
Your experience in numerical linear algebra will greatly benefit from a solid background in linear algebra. Your instructor recommends the following textbook as a helpful reference: Assorted links to additional material:
  • Lloyd N. Trefethen, The Definition of Numerical Analysis. [Link]
  • J. R. Shewchuk, The Conjugate Gradient Method without the Agonizing Pain. [Link]
Helpful links Important academic dates for this academic year

Announcements

Grading Information

The final grade will be composed of 25% homework and 75% final exam.
Your course grade will be determined by your cumulative average at the end of the quarter, based on the following scale:

A+ A A- B+ B B- C+ C C-
100 - 96.66 96.65 - 93.33 93.32 - 90.00 89.99 - 86.66 86.65 - 83.33 83.32 - 80.00 79.99 - 76.66 76.65 - 73.33 73.32 - 70

The above scale is guaranteed: for example, if your cumulative average is at least 85, then your final grade will be at least B. However, your instructor may adjust the above scale to be more generous.

Course Calendar

The dates of the exams, holidays, and an outline of topics to be discussed in each week. This calendar is preliminary and may be subject to change as the quarter progresses.
Week Topics
1 Introduction (Ch1)
2 Function spaces and Fourier transformation (App A)
Background in numerical linear algebra (App B)
3 Two-point boundary value problems (Ch2.1-3)
4 Elliptic Equations (Ch3.1-7)
Deadline to change grading option, change units, and drop classes without "W" grade on transcript.
5 Numerical methods for elliptic equations (Ch4, Ch5.1-4)
6 Systems of ordinary differential equations (Ch7)
Parabolic equations (Ch8.1.4)
Deadline to drop with "W" grade on transcript.
7 Numerical methods for paraboblic equations (Ch9)
8 Numerical methods for paraboblic equations (Ch10)
9 Hyperbolic Equations (Ch11) Numerical methods for hyperbolic equations (Ch12)
10 Numerical methods for hyperbolic equations (Ch12) Numerical methods for hyperbolic equations (Ch13)
FI
10.06.2021.
Final Exam. Details to be announced.