Introduction to Real Analysis
Natural, integer, rational, real numbers. Topology notions. Sequences and series. Sequence and series limits. Power series. Real functions of a variable. Local and global behavior. Limit and continuity of functions. Uniform continuity. Intermediate value theorem. Differentiation: local and global properties. Linearization and convexity. Taylor approach. Riemann integral. Fundamental Theorem of Calculus.
Basic Information
Workload
60 hours
Requirements
Calculus in One Real Variable
Mandatory:
- Mattuck, Arthur. Introduction to Analysis. MIT, Prentice Hall, 2013.
- Lima, Elon Lages. Análise Real, volume 1. University Mathematical Collection. IMPA.
- Lima, Elon Lages. Analysis Course. IMPA.
Complementary:
- Ávila, Geraldo. Introduction to Mathematical Analysis. Edgard Blucher.
- Bartle, R. G. The elements of real analysis.Wiley.
- Rudin, W. Principles of mathematical analysis.
- Abbot, S. Understanding analysis. Spring.
- Fulks, Watson. Advanced Calculus: An Introduction to Analysis. John Wiley and Sons, 1978.