Math 210A: Mathematical Methods in Physical Sciences and Engineering (Part A) - Bo Li

## Math 210A: Mathematical Methods in Physical Sciences and Engineering (Part A)

### General Course Information

 Prerequisites Calculus and linear algebra. Textbook Sadri Hassani, Mathematical Physics, A modern introduction to its foundation, Springer, 2006. Lectures 3:00 - 3:50, Mondays, Wednesdays, and Fridays, AP&M 5402. Instructor Bo Li Office: AP&M 5723. Office phone: (858) 534-6932. E-mail: bli@math.ucsd.edu. Office hours: 4:00 - 4:45 Mondays and Fridays. Teaching assistant Joey Reed Office: AP&M 5801. E-mail: j2reed@math.ucsd.edu. Office hours: 3:00 - 4:00, Thursdays. Class web page http://www.math.ucsd.edu/~bli/teaching/math210Af09/ Homework Homework will be assigned, collected, and graded. Exams There will be a final exam. Time: 3:00 - 5:59, Friday, December 11. Place: AP&M 5402. Grading The final course grade will be determined mainly based on the homework (45%), exam (45%), and class participation (10%).

### Homework

Assignment 1, due Friday, 10/9/09: PDF
Assignment 2, due Friday, 10/23/09: PDF
Assignment 3, due Friday, 11/6/09: PDF
Assignment 4, due Friday, 11/20/09: PDF
Assignment 5, due Friday, 12/4/09: PDF

### A Tentative Course Outline

Math 210A
1. advanced linear algebra and matrix theory
2. Hilbert spaces, orthogonal polynomials, and Fourier analysis, approximation theory
3. operators on Hilbert spaces, integral equations, Sturm-Liouville systems

Math 210B
1. complex analysis: analytical functions, integration and series, calculus of residues
2. partial differential equations: separation of variables, spherical harmonics
3. generalized functions, Green's functions
4. ordinary differential equations

Math 210C
1. stochastic processes
2. group theory, tensor algebra
3. differential geometry: vector fields, curvature, Riemannian manifolds, geodesics

### Some References (to be completed)

General

Advanced Linear Algebra and Matrix Theory
1. J. N. Franklin, Matrix Theory, Prentice-Hall, 1968.
2. W. Greub, Linear Algebra, 4th ed., Springer-Verlag, 1975.
3. P. Halmos, Finite Dimentional Vector Spaces, 2nd ed., Van Nostrand, 1958.
4. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
Hilbert Spaces and Operator Theory
1. R. E. Edwards, Functional Analysis, Dover, 1994.
2. G. Helmberg, Introduction to Spectral Theory in Hilbert Space, North-Holland, 1969.
3. E. Kreyszig, Introductory Functional Analysis with Applications, Joh Wiley & Sons, 1978.
4. F. Riesz and B. Sz.-Nagy, Functional Analysis, Dover, 1990.
Orthogonal Polynomials
Fourier Series and Integrals
Distributions
Complex Analysis
1. L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1953.
Ordinary Differential Equations and Dynamical Systems
Partial Differential Equations
Group Theory
Differential Geometry

Last updated by Bo Li on September 28, 2009.