MATH704 Analysis II Spring 2022

## Course Information

 Instructor Dr. Changhui Tan Lectures T Th 1:15pm - 2:30pm, at Coliseum 3007 Office Coliseum 2026N Office Hours M 11:00am - 12:00pm (via Blackboard), Th 11:30am - 12:30pm (in office), or by appointment Textbooks Terence Tao, An Introduction to Measure Theory, American Mathematical Society, 2011. (ISBN: 978-1-4704-6640-4) Syllabus Click Here

## Course Description

• The official course description for the MATH 703/704 sequence:
• Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. $$L^p$$ spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.
• List of Topics (for MATH 704):

## Homework Assignments

• Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday in class.
• The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
• Last update: 1/18, Homework 1 is available, due on Tuesday 1/25 in class.

## Exams

• There will be two 75 minutes in-class midterm exams. The tentative dates are February 22nd and April 12th. There will be a 150 minutes cumulative final exam.
• Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck!