/LC.GIF&client=easterncarolinaedu)
The real numbers and real analysis / Ethan D. Bloch.
| Author/creator | Bloch, Ethan D., 1956- |
| Format | Electronic |
| Publication Info | New York : Springer, |
| Description | xxviii, 553 p. : ill. ; 24 cm. |
| Supplemental Content | Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2011 English International |
| Supplemental Content | Full text available from Springer Books |
| Subjects |
| Contents | Construction of the real numbers: Introduction ; Entry 1: Axioms for the natural numbers ; Constructing the integers ; Entry 2: Axioms for the integers ; Constructing the rational numbers ; Dedekind cuts ; Constructing the real numbers ; Historical remarks -- Properties of the real numbers: Introduction ; Entry 3: Axioms for the real numbers ; Algebraic properties of the real numbers ; Finding the natural numbers, the integers and the rational numbers in real numbers ; Induction and recursion in practice ; The least upper bound property and its consequences ; Uniqueness of the real numbers ; Decimal expansion of real numbers ; Historical remarks -- Limits and continuity: Introduction ; Limits of functions ; Continuity ; Uniform continuity ; Two important theorems ; Historical remarks -- Differentiation: Introduction ; The derivative ; Computing derivatives ; The mean value theorem ; Increasing and decreasing functions, Part 1: Local and global extrema ; Increasing and decreasing functions, Part II: Further topics ; Historical remarks -- Integration: Introduction ; The Riemann integral ; Elementary properties of the Riemann integral ; Upper sums and lower sums ; Further properties of the Riemann integral ; Fundamental theorem of calculus ; Computing antiderivatives ; Lebesgue's theorem ; Area and arc length ; Historical remarks -- Limits to infinity: Introduction ; Limits to infinity ; Computing limits to infinity ; Improper integrals ; Historical remarks -- Transcendental functions: Introduction ; Logarithmic and exponential functions ; Trigonometric functions ; More about [Pi] ; Historical remarks -- Sequences: Introduction ; Sequences ; Three important theorems ; Applications of sequences ; Historical remarks -- Series: Introduction ; Series ; Convergence tests ; Absolute convergence and conditional convergence ; Power series as functions ; Historical remarks -- Sequences and series of functions: Introduction ; Sequences of functions ; Series of functions ; Functions as power series ; A continuous but nowhere differentiable function ; Historical remarks. |
| Bibliography note | Includes bibliographical references (p. 539-543) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Issued in other form | Electronic version: Real numbers and real analysis. New York : Springer, 2011 9780387721774 |
| Genre/form | Electronic books. |
| LCCN | 2011928556 |
| ISBN | 9780387721767 (hdbk. : acid-free paper) |
| ISBN | 0387721762 (hdbk. : acid-free paper) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | ✔ Available |