MTHS 644
Foundations of Analysis
James Reid
| 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. | |