Screen LibraryIntroduction to calculus and classical analysis
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| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Published: |
Springer,
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| Publisher Address: | New York |
| Publication Dates: | c2007. |
| Literature type: | Book |
| Language: | English |
| Edition: | 2nd ed. |
| Series: |
Undergraduate texts in mathematics. |
| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1007/978-0-387-69316-3 |
| Carrier Form: | x, 338 p.: ill. ; 24 cm. |
| ISBN: |
9780387693163 (electronic bk.) 0387693165 (electronic bk.) |
| Index Number: | O172 |
| CLC: | O172 |
| Contents: |
Includes bibliographical references (p. [331]) and index. 1. The set of real numbers. Sets and mappings -- The set R -- The subset N and the principle of induction -- The completeness property -- Sequences and limits -- Nonnegative series and decimal expansions -- Signed series and Cauchy sequences -- 2. Continuity. Compactness -- Continuous limits -- Continuous functions -- 3. Differentiation. Derivatives -- Mapping properties -- Graphing techniques -- Power series -- Trigonometry -- Primitives -- 4. Integration. The Cantor set -- Area -- The integral -- The fundamental theorem of calculus -- The method of exhaustion -- 5. Applications. Euler's gamma function -- The number [Greek letter pi] -- Gauss' arithmetic-geometric mean (AGM) -- The Gaussian integral -- Stirling's approximation of n! -- Infinite products -- Jacobi's theta functions -- Riemann's zeta function -- The Euler-Maclaurin formula -- A. Solutions. A.1. Solutions to Chapter 1 -- A.2. Solutions to Chapter 2 -- A.3. Solutions to Chapter 3 -- A.4. Solutions to Chapter 4 -- A.5. Solutions to Chapter 5 -- References -- Index. |