| This syllabus is tentative and
subject to revision |
| Text |
| 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.)
(Notes) |
| Meeting 7 |
The Riemann Integral -- Definition, existence
-Fundamental Theorem of Calculus (Chapter 6) |
| Meeting 8 |
The Log and Exponential functions - Applications
(Notes) |
| Meeting 9 |
Techniques of integration
(Notes) |
| Meeting 10 |
Infinite series, power series, Taylor series
-Tests for convergence (Chapter 7 & Notes) |
| Meeting 11 |
Applications
(Notes) |
| Meeting 12 |
The Trigonometric functions
(Notes) |
| Note: Notes will be provided to
flesh out the discussion as we go along in all cases, in addition to those
explicitly noted. |
