The Resource A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource)
A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource)
Resource Information
The item A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature. This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real‐valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self‐contained proof of the Fundamental Theorem of Algebra. In addition to the usual prerequisites for a first course in single‐variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting. From reviews: [The first edition is] a rigorous, wellpresented and original introduction to the core of undergraduate mathematics — firstyear calculus. It develops this subject carefully from a foundation of highschool algebra, with interesting improvements and insights rarely found in other books. [...] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz.
 Language
 eng
 Edition
 2nd ed. 2018.
 Extent
 1 online resource (IX, 538 pages)
 Contents

 1. Numbers and Functions
 2. Sequences
 3. Continuity and Limits
 4. Differentiation
 5. Applications of Differentiation
 6. Integration
 7. Elementary Transcendental Functions
 8. Applications and Approximations of Riemann Integrals
 9. Infinite Series and Improper Integrals
 10. Sequences and Series of Functions, Integrals Depending on a Parameter
 A. Construction of the Real Numbers
 B. Fundamental Theorem of Algebra
 References
 List of Symbols and Abbreviations
 Index
 Isbn
 9783030014001
 Label
 A Course in Calculus and Real Analysis
 Title
 A Course in Calculus and Real Analysis
 Statement of responsibility
 by Sudhir R. Ghorpade, Balmohan V. Limaye
 Language
 eng
 Summary
 Offering a unified exposition of calculus and classical real analysis, this textbook presents a meticulous introduction to single‐variable calculus. Throughout, the exposition makes a distinction between the intrinsic geometric definition of a notion and its analytic characterization, establishing firm foundations for topics often encountered earlier without proof. Each chapter contains numerous examples and a large selection of exercises, as well as a “Notes and Comments” section, which highlights distinctive features of the exposition and provides additional references to relevant literature. This second edition contains substantial revisions and additions, including several simplified proofs, new sections, and new and revised figures and exercises. A new chapter discusses sequences and series of real‐valued functions of a real variable, and their continuous counterpart: improper integrals depending on a parameter. Two new appendices cover a construction of the real numbers using Cauchy sequences, and a self‐contained proof of the Fundamental Theorem of Algebra. In addition to the usual prerequisites for a first course in single‐variable calculus, the reader should possess some mathematical maturity and an ability to understand and appreciate proofs. This textbook can be used for a rigorous undergraduate course in calculus, or as a supplement to a later course in real analysis. The authors’ A Course in Multivariable Calculus is an ideal companion volume, offering a natural extension of the approach developed here to the multivariable setting. From reviews: [The first edition is] a rigorous, wellpresented and original introduction to the core of undergraduate mathematics — firstyear calculus. It develops this subject carefully from a foundation of highschool algebra, with interesting improvements and insights rarely found in other books. [...] This book is a tour de force, and a necessary addition to the library of anyone involved in teaching calculus, or studying it seriously. N.J. Wildberger, Aust. Math. Soc. Gaz.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Ghorpade, Sudhir R
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Limaye, Balmohan V
 Series statement

 Undergraduate Texts in Mathematics,
 Springer eBooks
 Springer eBooks.
 http://library.link/vocab/subjectName

 Calculus
 Mathematics
 Sequences (Mathematics)
 Label
 A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Numbers and Functions  2. Sequences  3. Continuity and Limits  4. Differentiation  5. Applications of Differentiation  6. Integration  7. Elementary Transcendental Functions  8. Applications and Approximations of Riemann Integrals  9. Infinite Series and Improper Integrals  10. Sequences and Series of Functions, Integrals Depending on a Parameter  A. Construction of the Real Numbers  B. Fundamental Theorem of Algebra  References  List of Symbols and Abbreviations  Index
 Control code
 9783030014001
 Dimensions
 unknown
 Edition
 2nd ed. 2018.
 Extent
 1 online resource (IX, 538 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030014001
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1076485334
 Label
 A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1. Numbers and Functions  2. Sequences  3. Continuity and Limits  4. Differentiation  5. Applications of Differentiation  6. Integration  7. Elementary Transcendental Functions  8. Applications and Approximations of Riemann Integrals  9. Infinite Series and Improper Integrals  10. Sequences and Series of Functions, Integrals Depending on a Parameter  A. Construction of the Real Numbers  B. Fundamental Theorem of Algebra  References  List of Symbols and Abbreviations  Index
 Control code
 9783030014001
 Dimensions
 unknown
 Edition
 2nd ed. 2018.
 Extent
 1 online resource (IX, 538 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783030014001
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1076485334
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/ACourseinCalculusandRealAnalysisbySudhir/lMQQBUb8Jus/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/ACourseinCalculusandRealAnalysisbySudhir/lMQQBUb8Jus/">A Course in Calculus and Real Analysis, by Sudhir R. Ghorpade, Balmohan V. Limaye, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>