Normal view MARC view

Elementary analysis: the theory of calculus

Author: Ross, Kenneth A. Series: Undergraduate texts in mathematics Publisher: Springer, 1980.Language: EnglishDescription: 351 p. : Graphs ; 24 cm.ISBN: 038790459XType of document: BookBibliography/Index: Includes bibliographical references and index
Tags: No tags from this library for this title. Log in to add tags.
Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA303 .R67 1980
(Browse shelf)
001175136
Available 001175136
Total holds: 0

Includes bibliographical references and index

Digitized

Elementary Analysis: the Theory of Calculus Contents Preface 1 Introduction 1 The Set N of Natural Numbers .......................................... 2 The Set Q of Rational Numbers ......................................... 3 The Set R of Real Numbers ............................................... 4 The Completeness Axiom .................................................. 5 The Symbols +oo and --oo ................................................ 6 * A Development of R......................................................... 2 Sequences 7 Limits of Sequences .......................................................... 8 A Discussion about Proofs ................................................ 9 Limit Theorems for Sequences........................................... 10 Monotone Sequences and Cauchy Sequences . ..................... 11 Subsequences................................................................... 12 lim sup's and lim inf's .......................................................... 13 * Some Topological Concepts in Metric Spaces ...................... 14 Series ............................................................................... 15 Alternating Series and Integral Tests .................................... 16 * Decimal Expansions of Real Numbers ................................ v 1 1 6 12 19 27 28 31 31 37 43 54 63 75 79 90 100 105 x Contents 3 Continuity 115 17 Continuous Functions .................................................... 115 18 Properties of Continuous Functions ................................ 126 19 Uniform Continuity ......................................................... 132 20 Limits of Functions ......................................................... 145 21 * More on Metric Spaces: Continuity ......................... 156 22 * More on Metric Spaces: Connectedness ........................ 164 4 Sequences and Series of Functions 171 23 Power Series ................................................................... 171 24 Uniform Convergence ..................................................... 177 25 More on Uniform Convergence ........................................ 184 26 Differentiation and Integration of Power Series . .............. 192 27 * Weierstrass's Approximation Theorem .......................... 200 5 Differentiation 205 28 Basic Properties of the Derivative .................................... 205 29 The Mean Value Theorem ............................................... 213 30 * L'Hospital's Rule ..................................................... 222 31 'Taylor's Theorem ...................................................... 230 6 Integration 243 32 The Riemann Integral ..................................................... 243 33 Properties of the Riemann Integral .................................. 253 34 Fundamental Theorem of Calculus ................................. 261 35 * Riemann-Stieltjes Integrals ..................................... 268 36 * Improper Integrals......................................................... 292 37 * A Discussion of Exponents and Logarithms . ................ 299 Appendix on Set Notation Selected Hints and Answers References Symbols Index Index 309 311 341 345 347

There are no comments for this item.

Log in to your account to post a comment.
Koha 18.11 - INSEAD Catalogue
Home | Contact Us | What's Koha?