Real analysis

Basic information

Workload: 

90 hours

Prerequisite: 

CALCULUS IN ONE REAL VARIABLE, Fundamentals of Mathematics

Syllabus: 

Natural, integer, rational, real numbers. Topology notions. Sequences and series. Sequence and series limits. Power series. One variable real functions. Local and global behavior. Limit and continuity of functions. Uniform continuity. Intermediate value theorem. Differentiation: local and global properties. Linearization and convexity. Taylor approximation. Riemann integral. Fundamental Theorem of Calculus.

 

Teaching Plan

Bibliography

Mandatory: 

•    Mattuck, Arthur. Introduction to Analysis. MIT, P1rentice Hall, 1999.
•    Lima, Elon Lages. Real Analysis, volume 1. University Mathematical Collection, IMPA.
•    Denliger, Charles G. Elements of Real Analysis. Jones and Bartlett Publishers, 2011.

Complementary: 

•    Ávila, Geraldo. Introduction to Mathematical Analysis. Edgard Blucher.
•    Bartle, R. G. Elements of Real Analysis. Campus Publisher.
•    Rudin, R. Principles of Mathematical Analysis. The Technical Book.
•    Good, Ralph. A primer of real functions. The Carus Mathematical Monographs.
•    Fulks, Watson. Advanced Calculus: An Introduction to Analysis. John Wiley and Sons, 1967.