MTHS 644
Foundations of Analysis

James Reid

This syllabus is tentative and subject to revision
Maxwell Rosenlicht, Introduction to Analysis (Dover Publications), Paperback
Course Schedule
Meeting 1 Sets & functions
-the real numbers (Chapters 1,2)
Meeting 2 Limits, convergent sequences
-the topology of the line (Chapters 2,3)
Meeting 3 More on topology-compactness & connectedness
-continuity of functions (Chapters 2,3)
Meeting 4 More on continuous functions
Meeting 5 Derivatives (Definition, geometric interpretation, rules of use Mean value theorem)
(Chapter 5)
Meeting 6 Applications (Max/min problems, related rates, etc.)
Meeting 7 The Riemann Integral -- Definition, existence
-Fundamental Theorem of Calculus (Chapter 6)
Meeting 8 The Log and Exponential functions - Applications
Meeting 9 Techniques of integration
Meeting 10 Infinite series, power series, Taylor series
-Tests for convergence (Chapter 7 & Notes)
Meeting 11 Applications
Meeting 12 The Trigonometric functions
Note: Notes will be provided to flesh out the discussion as we go along in all cases, in addition to those explicitly noted.