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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: 9/16, Homework 3 updated, due date on Tuesday 9/21. Homework 4 is available, due on Tuesday 9/28.
  •  Download Homework Assignments.

 

Exams

  • There will be two 75 minutes in-class midterm exams. The tentative dates are September 28th and November 9th. 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! 

 

Grades

  • Your grade are distributed as below:
  • Homework » 30%
    Midterms » 20% each
    Final exam » 30%
  • You can monitor your grades via Blackboard.

 

Contact Information

  • Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.