MATH703 Analysis I Fall 2021

## Course Information

 Instructor Dr. Changhui Tan Lectures T Th 11:40am - 12:55pm, at Coliseum 3006B Office Coliseum 2026N Office Hours T Th 10:00am - 11:00am, or by appointment Textbooks R.H. Dyer and D.E. Edmunds, From Real to Complex Analysis, Springer International Publishing, 2014. (ISBN: 978-3-319-06208-2) A. Schep, Complex Script, lecture notes. 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 703):

## 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: 11/17, Homework 8 is available.

## Exams

• There will be two 75 minutes in-class midterm exams. The tentative dates are September 28th and November 11th. 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!
• Last update: 11/17, midterm 2 is available.