Real AnalysisAmerican Mathematical Soc., 2005 - 151 pages Morgan builds the theory behind calculus from the basic concepts of real numbers, limits, and open and closed sets, and includes proofs and exercises for the undergraduate student. He covers real numbers and limits, including the concepts of infinity and sequences, topology, including the Cantor set and fractals, and then progresses to calculus, in |
Contents
Calculus | 14 |
Sequences | 15 |
Chapter | 20 |
Chapter | 26 |
Open and Closed Sets | 29 |
Compactness | 43 |
The Cantor Set and Fractals | 57 |
Chapter 27 | 125 |
Partial Solutions to Exercises | 141 |
Greek Letters | 151 |
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Common terms and phrases
accumulation point analysis answer assume ball boundary point bounded calculus called Cantor set Cauchy Chapter choose closed sets compact set connected consider constant contained continuous function contradiction converges absolutely Corollary countable course decimal place defined definition derivative differentiable disjoint distance diverges domain elements equal equicontinuity Exercises exists exp(x f is continuous Figure finite subcover formula Fourier series function f give a counterexample Give an example given hence hold implies includes infinitely integral intersection interval largest length letter limit maximum Mean Value Theorem means metric space negative nonempty Note open cover open sets positive Proof Proposition Prove radius radius of convergence rationals real numbers Riemann integral Riemann sums sequence series converges Similarly subsequence subset Suppose third true uniform uniformly continuous union unit