Real Analysis II FA15

Dear students, welcome to the undergraduate course in Real Analysis II!

ANNOUNCEMENTS:

Dear students, there will be a presentation assignment in the class dated December 28, 2015.

Presentations_1_RA_SP15

Assignment # 4 is missing from FA12-BSM-021.

 

Course Module Real Analysis II Fall 2015

Assignement # 1: Pointwise convergence of sequence and series of functions

Assignment # 2: Uniform convergence of sequence of functions

Assignment # 3: Uniform convergence of sequence and series of functions, Uniform convergence and continuity, uniform convergence and Integration, uniform convergence and Differentiation, Stone Weierstrass Theorem.

Assignment # 4: Bolzano-Weierstrass property for sequence of functions, Arzela Ascoli Theorem, Analytic functions, Abel’s Theorem

 

Lecture # 4: Uniform Convergence, Cauchy criterion, Weierstrass M-test

Lecture # 5: Abel’s test, Dirichlet’s test

 

 

 

 

 

 

 

 

 

 

NOTE: The lectures, assignments and quizzes above are loosely based on the following text books:

  Walter Rudin, Principles of Mathematical Analysis, Third Edition
  Douglass, Introduction to Mathematical Analysis, First Edition.
 Gaskil, Narayanaswami, Elements of Real Analysis, First Edition.                                                             Bartle & Sherebert, Introduction to Real Analysis, Third Edition.                                                                 Apostol, Mathematical Analysis, Second Edition.

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