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.
|Axioms for the Field (R) of Real Numbers|
|First Properties of (R)|
|Sequences of Real Numbers, Convergence|
|Special Subsets of (R)|
|Continuous Functions on an Interval|
|Limits of Functions|
|Beyond the Riemann Integral.|
|Table of Contents provided by Publisher. All Rights Reserved.|
Series: Undergraduate Texts in Mathematics
Number Of Pages: 240
Published: 16th March 1998
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5 x 1.91
Weight (kg): 0.5