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 space methods;
  • Complex variables techniques;
  • Ordinary differential equations and dynamical systems;
  • Partial differential equations: solution methods, analysis, and applications; and
  • Basics of probability and stochastic processes.

We will follow partially the following books:

  • Michael T. Vaughn, Introduction to Mathematical Physics, Wiley-VCH Verlag GmbH & Co. KGaA, 2007;
  • Philippe Dennery and Andre Krzywicki, Mathematics for Physicists, Dover, 2012.
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.

Spring 2018 Class Information

Topics Partial differential equations and their applications. Basics of stochastic process (if time permits).
Prerequisites Calculus, linear algebra, and basic ordinary differential equations.
Lectures 1:00 pm - 1:50 pm, Mondays, Wednesdays, and Fridays, AP&M B402A.
Instructor Bo Li
Office: AP&M 5723. Office phone: (858) 534-6932. E-mail: bli@math.ucsd.edu.
Office hours: 11:30 - 12:00 Thursdyas and 3:00 - 4:00 Fridays.
Teaching Assistant Mr. Yucheng Tu
Office: AP&M 5720. E-mail: y7tu@ucsd.edu.
Office hours: 3:00 - 5:00, Thursdays.
Class web page http://www.math.ucsd.edu/~bli/teaching/math210Cs18/
Course Material Lecture Notes
A List of References
Homework Homework will be assigned, collected, and partially graded every week. Homework papers will be collected at the begining of lecture on the due day, and the graded homework papers will be returned in the lecture within a week.
Exams Final exam: 8:00 am - 10:59 am, Wednesday, June 13, 2018. Place: To be announced.
Grading The final course grade will be determined based on homework 50% and final exam 50%.

Last updated by Bo Li on May 26, 2018.