Principles of Analysis -- Spring 1997
Principles of Analysis is a one-semester introductory real analysis
course for mathematics majors. The main goals are to introduce more
of the theory of the real number systema and to prove the main theorems
of one-variable calculus in a rigorous fashion. The topics we covered
included:
- Algebraic, order, and completeness properties of the real numbers
- Sequences, convergence
- Limits of functions
- Continuity and consequences:
- Extreme value theorem for continuous functions on closed intervals
- Intermediate Value Theorem
- Differentiability
- Mean Value Theorem and consequences
- The Riemann integral
- The Fundamental Theorem of Calculus
- Infinite series -- integral, comparison, ratio tests
Text: Bilodeau and Thie, Introduction to Analysis
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