Fall 2013: Methods of Applied Mathematics I

Course Numbers: MATH 383C/CSE 386C

Unique Numbers: 57585 and 68410

Meeting time and place: T TH 3:30 to 5:00 pm in RLM 5.120

Professor: Luis A. Caffarelli, RLM 10.150A (512)471-3160

Office Hours: T TH 2:00-3:00 pm

Teaching Assistant: Chenglong Zhang
Email: chenglong@ices.utexas.edu

Discussion Section: F 3:00 - 4:30 pm, RLM 5.114

Materials:
Each student is required to have a set of lecturer-prepared notes "Functional Analysis for the Applied Mathematician" by Todd Arbogast and Jerry Bona (2013 version) available from the UT Copy Center in Welch 2.228.

Homework, Exams, and Grades:
Homework will be assigned regularly. Students are encouraged to work in groups; however, each student must write up his or her own work. There will be three midterm exams and no final exam.

Exam 1: End of September
Exam 2: End of October
Exam 3: Beginning of December

Grading:
The course grade will be based on a total of 100 points. Each exam will count as 20 points and the homework taken together will count as 40 points.

Course Description:
This is the first semester of a course on methods of applied mathematics. It is open to mathematics, science, engineering, and finance students. It is suitable to prepare graduate students for the Applied Mathematics Preliminary Exam in mathematics and the Area A Preliminary Exam in CSEM. The first semester is an introduction to functional analysis.

Preliminaries (2 lectures)

Normed Linear Spaces and Banach Spaces (10 to 12 lectures)

Hilbert Spaces (about 4 lectures)

Spectral Theory and Compact Operators (about 8 lectures)

Distributions (about 4 lectures)

The University of Texas at Austin honor code:
The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the university is expected to uphold these values through integrity, honesty, trust, fairness, and respect toward peers and community.

Students with Disabilities:
The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY. If you plan on using accomodation, you need to notify your instructor early in the semester.

Emergency Classroom Evacuation:
Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside. Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building. Do not re-enter a building unless given instructions by the Austin Fire Department, the University Police Department, or the Fire Prevention Services office.

Religious Holidays:
The University of Texas at Austin provides upon request appropriate academic accommodations for religious holidays.