Introductory analysis :: a deeper view of calculus /
Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision,...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego :
Harcourt/Academic Press,
©2001.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstra. |
| Beschreibung: | 1 online resource (xvi, 201 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (page 197) and index. |
| ISBN: | 9780080549422 008054942X 1281028711 9781281028716 9786611028718 6611028714 |
Internformat
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| 245 | 1 | 0 | |a Introductory analysis : |b a deeper view of calculus / |c Richard J. Bagby. |
| 260 | |a San Diego : |b Harcourt/Academic Press, |c ©2001. | ||
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| 504 | |a Includes bibliographical references (page 197) and index. | ||
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| 505 | 0 | |a Cover; Copyright Page; Contents; Acknowledgments; Preface; Chapter I. The Real Number System; 1. Familiar Number Systems; 2. Intervals; 3. Suprema and Infima; 4. Exact Arithmetic in R; 5. Topics for Further Study; Chapter II. Continuous Functions; 1. Functions in Mathematics; 2. Continuity of Numerical Functions; 3. The Intermediate Value Theorem; 4. More Ways to Form Continuous Functions; 5. Extreme Values; Chapter III. Limits; 1. Sequences and Limits; 2. Limits and Removing Discontinuities; 3. Limits Involving infinity; Chapter IV. The Derivative; 1. Differentiability | |
| 505 | 8 | |a 2. Combining Differentiable Functions3. Mean Values; 4. Second Derivatives and Approximations; 5. Higher Derivatives; 6. Inverse Functions; 7. Implicit Functions and Implicit Differentiation; Chapter V. The Riemann Integral; 1. Areas and Riemann Sums; 2. Simplifying the Conditions for Integrability; 3. Recognizing Integrability; 4. Functions Defined by Integrals; 5. The Fundamental Theorem of Calculus; 6. Topics for Further Study; Chapter VI. Exponential and Logarithmic Functions; 1. Exponents and Logarithms; 2. Algebraic Laws as Definitions; 3. The Natural Logarithm | |
| 505 | 8 | |a 4. The Natural Exponential Function5. An Important Limit; Chapter VII. Curves and Arc Length; 1. The Concept of Arc Length; 2. Arc Length and Integration; 3. Arc Length as a Parameter; 4. The Arctangent and Arcsine Functions; 5. The Fundamental Trigonometric Limit; Chapter VIII. Sequences and Series of Functions; 1. Functions Defined by Limits; 2. Continuity and Uniform Convergence; 3. Integrals and Derivatives; 4. Taylor's Theorem; 5. Power Series; 6. Topics for Further Study; Chapter IX. Additional Computational Methods; 1. L'Hôpital's Rule; 2. Newton's Method; 3. Simpson's Rule | |
| 505 | 8 | |a 4. The Substitution Rule for IntegralsReferences; Index | |
| 520 | |a Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstra. | ||
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| author | Bagby, Richard J. |
| author_GND | http://id.loc.gov/authorities/names/nr00029591 |
| author_facet | Bagby, Richard J. |
| author_role | |
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| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 .B15 2001eb |
| callnumber-search | QA300 .B15 2001eb |
| callnumber-sort | QA 3300 B15 42001EB |
| callnumber-subject | QA - Mathematics |
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| contents | Cover; Copyright Page; Contents; Acknowledgments; Preface; Chapter I. The Real Number System; 1. Familiar Number Systems; 2. Intervals; 3. Suprema and Infima; 4. Exact Arithmetic in R; 5. Topics for Further Study; Chapter II. Continuous Functions; 1. Functions in Mathematics; 2. Continuity of Numerical Functions; 3. The Intermediate Value Theorem; 4. More Ways to Form Continuous Functions; 5. Extreme Values; Chapter III. Limits; 1. Sequences and Limits; 2. Limits and Removing Discontinuities; 3. Limits Involving infinity; Chapter IV. The Derivative; 1. Differentiability 2. Combining Differentiable Functions3. Mean Values; 4. Second Derivatives and Approximations; 5. Higher Derivatives; 6. Inverse Functions; 7. Implicit Functions and Implicit Differentiation; Chapter V. The Riemann Integral; 1. Areas and Riemann Sums; 2. Simplifying the Conditions for Integrability; 3. Recognizing Integrability; 4. Functions Defined by Integrals; 5. The Fundamental Theorem of Calculus; 6. Topics for Further Study; Chapter VI. Exponential and Logarithmic Functions; 1. Exponents and Logarithms; 2. Algebraic Laws as Definitions; 3. The Natural Logarithm 4. The Natural Exponential Function5. An Important Limit; Chapter VII. Curves and Arc Length; 1. The Concept of Arc Length; 2. Arc Length and Integration; 3. Arc Length as a Parameter; 4. The Arctangent and Arcsine Functions; 5. The Fundamental Trigonometric Limit; Chapter VIII. Sequences and Series of Functions; 1. Functions Defined by Limits; 2. Continuity and Uniform Convergence; 3. Integrals and Derivatives; 4. Taylor's Theorem; 5. Power Series; 6. Topics for Further Study; Chapter IX. Additional Computational Methods; 1. L'Hôpital's Rule; 2. Newton's Method; 3. Simpson's Rule 4. The Substitution Rule for IntegralsReferences; Index |
| ctrlnum | (OCoLC)173523352 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
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| discipline | Mathematik |
| format | Electronic eBook |
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| spelling | Bagby, Richard J. http://id.loc.gov/authorities/names/nr00029591 Introductory analysis : a deeper view of calculus / Richard J. Bagby. San Diego : Harcourt/Academic Press, ©2001. 1 online resource (xvi, 201 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (page 197) and index. Print version record. Cover; Copyright Page; Contents; Acknowledgments; Preface; Chapter I. The Real Number System; 1. Familiar Number Systems; 2. Intervals; 3. Suprema and Infima; 4. Exact Arithmetic in R; 5. Topics for Further Study; Chapter II. Continuous Functions; 1. Functions in Mathematics; 2. Continuity of Numerical Functions; 3. The Intermediate Value Theorem; 4. More Ways to Form Continuous Functions; 5. Extreme Values; Chapter III. Limits; 1. Sequences and Limits; 2. Limits and Removing Discontinuities; 3. Limits Involving infinity; Chapter IV. The Derivative; 1. Differentiability 2. Combining Differentiable Functions3. Mean Values; 4. Second Derivatives and Approximations; 5. Higher Derivatives; 6. Inverse Functions; 7. Implicit Functions and Implicit Differentiation; Chapter V. The Riemann Integral; 1. Areas and Riemann Sums; 2. Simplifying the Conditions for Integrability; 3. Recognizing Integrability; 4. Functions Defined by Integrals; 5. The Fundamental Theorem of Calculus; 6. Topics for Further Study; Chapter VI. Exponential and Logarithmic Functions; 1. Exponents and Logarithms; 2. Algebraic Laws as Definitions; 3. The Natural Logarithm 4. The Natural Exponential Function5. An Important Limit; Chapter VII. Curves and Arc Length; 1. The Concept of Arc Length; 2. Arc Length and Integration; 3. Arc Length as a Parameter; 4. The Arctangent and Arcsine Functions; 5. The Fundamental Trigonometric Limit; Chapter VIII. Sequences and Series of Functions; 1. Functions Defined by Limits; 2. Continuity and Uniform Convergence; 3. Integrals and Derivatives; 4. Taylor's Theorem; 5. Power Series; 6. Topics for Further Study; Chapter IX. Additional Computational Methods; 1. L'Hôpital's Rule; 2. Newton's Method; 3. Simpson's Rule 4. The Substitution Rule for IntegralsReferences; Index Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstra. English. Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast has work: Introductory analysis (Text) https://id.oclc.org/worldcat/entity/E39PCFDf3mtB9QBkQ8kwJ3mjYd https://id.oclc.org/worldcat/ontology/hasWork Print version: Bagby, Richard J. Introductory analysis. San Diego : Harcourt/Academic Press, ©2001 0120725509 9780120725502 (DLC) 00103265 (OCoLC)45316258 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=203257 Volltext |
| spellingShingle | Bagby, Richard J. Introductory analysis : a deeper view of calculus / Cover; Copyright Page; Contents; Acknowledgments; Preface; Chapter I. The Real Number System; 1. Familiar Number Systems; 2. Intervals; 3. Suprema and Infima; 4. Exact Arithmetic in R; 5. Topics for Further Study; Chapter II. Continuous Functions; 1. Functions in Mathematics; 2. Continuity of Numerical Functions; 3. The Intermediate Value Theorem; 4. More Ways to Form Continuous Functions; 5. Extreme Values; Chapter III. Limits; 1. Sequences and Limits; 2. Limits and Removing Discontinuities; 3. Limits Involving infinity; Chapter IV. The Derivative; 1. Differentiability 2. Combining Differentiable Functions3. Mean Values; 4. Second Derivatives and Approximations; 5. Higher Derivatives; 6. Inverse Functions; 7. Implicit Functions and Implicit Differentiation; Chapter V. The Riemann Integral; 1. Areas and Riemann Sums; 2. Simplifying the Conditions for Integrability; 3. Recognizing Integrability; 4. Functions Defined by Integrals; 5. The Fundamental Theorem of Calculus; 6. Topics for Further Study; Chapter VI. Exponential and Logarithmic Functions; 1. Exponents and Logarithms; 2. Algebraic Laws as Definitions; 3. The Natural Logarithm 4. The Natural Exponential Function5. An Important Limit; Chapter VII. Curves and Arc Length; 1. The Concept of Arc Length; 2. Arc Length and Integration; 3. Arc Length as a Parameter; 4. The Arctangent and Arcsine Functions; 5. The Fundamental Trigonometric Limit; Chapter VIII. Sequences and Series of Functions; 1. Functions Defined by Limits; 2. Continuity and Uniform Convergence; 3. Integrals and Derivatives; 4. Taylor's Theorem; 5. Power Series; 6. Topics for Further Study; Chapter IX. Additional Computational Methods; 1. L'Hôpital's Rule; 2. Newton's Method; 3. Simpson's Rule 4. The Substitution Rule for IntegralsReferences; Index Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082116 |
| title | Introductory analysis : a deeper view of calculus / |
| title_auth | Introductory analysis : a deeper view of calculus / |
| title_exact_search | Introductory analysis : a deeper view of calculus / |
| title_full | Introductory analysis : a deeper view of calculus / Richard J. Bagby. |
| title_fullStr | Introductory analysis : a deeper view of calculus / Richard J. Bagby. |
| title_full_unstemmed | Introductory analysis : a deeper view of calculus / Richard J. Bagby. |
| title_short | Introductory analysis : |
| title_sort | introductory analysis a deeper view of calculus |
| title_sub | a deeper view of calculus / |
| topic | Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Analyse mathématique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Mathematical analysis fast |
| topic_facet | Mathematical analysis. Analyse mathématique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Mathematical analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=203257 |
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