Math 210: Mathematical Methods in Physical Sciences and Engineering, 2017-2018, - Bo Li

Math 210: Mathematical Methods in Physical Sciences and Engineering
Fall 2017, Winter 2018, and Spring 2018

Instructor: Bo Li
Office: AP&M 5723. Office phone: (858) 534-6932. Email: bli@math.ucsd.edu

This is a year-long (three-quarter) course designed for graduate students and upper-division undergraduate students of applied and computational mathematics, physical sciences, and engineering. The course covers the basics of broadly ranged important topics of modern mathematics that have emerging applications in science and engineering. An emphasis will be placed on both the mathematical rigor and problem solving techniques. Examples of applications, particularly of those related to research at UC San Diego, will be presented. Numerical methods will be discussed briefly along the course but will not be covered in depth. It is expected that students who take this course seriously will be able to build a solid mathematical background for scientific, engineering, mathematical, and interdisciplinary researches.

Prerequisites of this course is a solid background of calculus and linear algebra. Homework will be assigned, collected, and graded weekly. Course grades will be based on homework and exams.

Topics of the course include but are not limited to:

  • Sequences and series of functions and matrix techniques;
  • Approximation theory and Hilbert spaces methods;
  • Complex variables techniques;
  • Ordinary differential equations and dynamical systems;
  • Partial differential equations: solution methods, analysis, and applications; and
  • Basics of stochastic processes.

We will follow partially the following books:

  • Michael T. Vaughn, Introduction to Mathematical Physics, Wiley-VCH Verlag GmbH & Co. KGaA, 2007. (This will be used partially as a textbook and a main reference book.)
  • Philippe Dennery and Andre Krzywicki, Mathematics for Physicists, Dover, 2012. (This will be used as a supplemental book.)
Supplemental lecture notes will be distributed in the class. More rferences will be listed in the class webpage and some of them will be reserved in UCSD library.

Fall Quarter 2017 Class Information

Prerequisites Calculus and linear algebra.
Lectures 1:00 pm - 1:50 pm, Mondays, Wednesdays, and Fridays, AP&M 2402.
Instructor Bo Li
Office: AP&M 5723. Office phone: (858) 534-6932. E-mail: bli@math.ucsd.edu.
Office hours: 2:00 pm - 2:45 pm Mondays and Wednesdays.
Teaching Assistant Mr. Benjamin Ciotti
Office: AP&M 5712. E-mail: bciotti@ucsd.edu
Office hours: 4:00 pm - 5:00 pm, Mondays and Thursdays.
Class web page http://www.math.ucsd.edu/~bli/teaching/math210Af17/
Course Material
Homework Homework will be assigned, collected, and partially graded every week. Homework papers will be collected at the begining of Friday's lecture, and the graded homework papers will be returned in the lecture of the following Friday.
Exams There will be a midterm exam and a final exam. Both will be close-book, close-note, and no-calculator exams.
    Midterm exam: 1:00 pm, - 1:50 pm, Friday, November 3, 2017, AP&M 2402.
    Final exam: 11:30 am - 2:29 pm, Monday, December 11, 2017. Place to be announced.
Note: neither rescheduled nor make-up exams will be allowed unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.
Grading The final course grade will be determined based on homework 20%, midterm exam 30%, and final exam 50%.

Last updated by Bo Li on October 30, 2017.