Concepts of Real Analysis
Schedule of classes: M W F 9:05 AM - 9:55 PM in 173 WILLARD (Sched. \# 597391)
Office Hours (tentative): Monday 4:30 - 6 PM & Tuesday 5 - 6:30 PM
Topics: (sections are from the textbook, Brannan's A first Course in Mathematical Analysis)
- Chapter 1, Real Numbers: Review of properties of real numbers (Sections 1.1.1,1.1.2,1.2.1,1.2.2,1.5), irrational numbers (1.1.3), modulus and distance (1.2.3), triangle inequality, Bernoulli and Cauchy-Schwartz inequalities (1.3), sumpremum and infimum, completeness (1.4), Archimedean and density properties (1.1.4).
- Chapter 2, Sequences: monotonic sequences (2.1), null sequences (2.2), convergent and divergent sequences (2.3, 2.4), the Monotone Convergence Theorem (2.5).
- Chapter 3, Series: definition and examples, geometric series, telescoping series, non-null test (3.1), series of positive terms, comparison, root and ratio, Cauchy tests (3.2), alternating series, rearrangements, products (3.3), the exponential function (3.4).
- Chapter 4, Continuity
- Chapter 5, Limits
© Anna Mazzucato Last modified: Thur Jan 7 15:23:29 EDT 2015