Time: MWF 10:00-1:50pm
Location: Altgeld Hall 242Instructor: Marius Junge
I: Real Numbers
What are real numbers?; sets, maps, functions, cardinality; Natural numbers, equivalence relations, integers, rational numbers, fields, ordered fields; complete ordered fields.
Limits, monotone sequences, subsequences, Bolzano-Weierstrass, limsup and liminf, series.
III: Continuous Functions
Definition and permanence properties, uniform continuity, removing singularities, monotonicity, inverse function and intermediate alue theorem
Basic rules, mean value theorem and taylor
Different definition and Fundamental Theorems. Applications.
V: Power Series
Interchanging limits, examples.
Elementary Analysis: The Theory of Calculus by Kenneth Ross, 2 edition, SpringerGrading:
Midterm1 September 27
Midterm2 October 24
Midterm2 November 15 (if necessary-probably take home)
Final: see uncombined schedule
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