Real Analysis
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.
Basic Information
Workload
90 hours
Requirements
CALCULUS IN ONE REAL VARIABLE, Fundamentals of Mathematics
Mandatory:
- Mattuck, Arthur. Introduction to Analysis. MIT, P1rentice Hall, 1999.
- Lima, Elon Lages. Análise Real, 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.