Real Analysis (Boman and Rogers)
- Page ID
- 8056
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The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.
Front Matter
1: Numbers - Real (ℝ) and Rational (ℚ)
2: Calculus in the 17th and 18th Centuries
3: Questions Concerning Power Series
4: Convergence of Sequences and Series
5: Convergence of the Taylor Series- A “Tayl” of Three Remainders
6: Continuity - What It Isn’t and What It Is
7: Intermediate and Extreme Values
8: Back to Power Series
9: Back to the Real Numbers
10: Epilogue to Real Analysis
Back Matter
Thumbnail: Real number line with some constants such as \(\pi\). (Public Domain; User:Phrood).