A First Course in Real Analysis /
The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1994.
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| Series: | Undergraduate texts in mathematics.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | The book offers an initiation into mathematical reasoning, and into the mathematician's mind-set and reflexes. Specifically, the fundamental operations of calculus--differentiation and integration of functions and the summation of infinite series--are built, with logical continuity (i.e., "rigor"), starting from the real number system. The first chapter sets down precise axioms for the real number system, from which all else is derived using the logical tools summarized in an Appendix. The discussion of the "fundamental theorem of calculus," the focal point of the book, especially thorough. The concluding chapter establishes a significant beachhead in the theory of the Lebesgue integral by elementary means. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xi, 240 pages) |
| ISBN: | 9781441985484 (electronic bk.) 1441985484 (electronic bk.) |
| ISSN: | 0172-6056 |