A Course in Calculus and Real Analysis / Sudhir R. Ghorpade (2006)  

Público ISBD Título : A Course in Calculus and Real Analysis Tipo de documento: documento electrónico Autores: Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: X, 432 p Il.: online resource ISBN/ISSN/DL: 978-0-387-36425-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Functions  of  real  variables  Sequences  Real  Sequences,  Series,  Summability Clasificación: 51 Matemáticas Resumen: This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature Nota de contenido: Numbers and Functions -- Sequences -- Continuity and Limits -- Differentiation -- Applications of Differentiation -- Integration -- Elementary Transcendental Functions -- Applications and Approximations of Riemann Integrals -- Infinite Series and Improper Integrals En línea: http://dx.doi.org/10.1007/0-387-36425-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34830 A Course in Calculus and Real Analysis [documento electrónico] / Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye . - New York, NY : Springer New York, 2006 . - X, 432 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) . ISBN : 978-0-387-36425-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Functions  of  real  variables  Sequences  Real  Sequences,  Series,  Summability Clasificación: 51 Matemáticas Resumen: This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis. The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature Nota de contenido: Numbers and Functions -- Sequences -- Continuity and Limits -- Differentiation -- Applications of Differentiation -- Integration -- Elementary Transcendental Functions -- Applications and Approximations of Riemann Integrals -- Infinite Series and Improper Integrals En línea: http://dx.doi.org/10.1007/0-387-36425-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34830

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A Course in Multivariable Calculus and Analysis / Sudhir R. Ghorpade (2010)  

Público ISBD Título : A Course in Multivariable Calculus and Analysis Tipo de documento: documento electrónico Autores: Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XII, 475 p. 65 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-1621-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics) Clasificación: 51 Matemáticas Resumen: This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments’’ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus Nota de contenido: Vectors and Functions -- Sequences, Continuity, and Limits -- Partial and Total Differentiation -- Applications of Partial Differentiation -- Multiple Integration -- Applications and Approximations of Multiple Integrals -- Double Series and Improper Double Integrals En línea: http://dx.doi.org/10.1007/978-1-4419-1621-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33601 A Course in Multivariable Calculus and Analysis [documento electrónico] / Sudhir R. Ghorpade ; SpringerLink (Online service) ; Balmohan V. Limaye . - New York, NY : Springer New York, 2010 . - XII, 475 p. 65 illus. in color : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) . ISBN : 978-1-4419-1621-1 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics) Clasificación: 51 Matemáticas Resumen: This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus. This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point. Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments’’ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus Nota de contenido: Vectors and Functions -- Sequences, Continuity, and Limits -- Partial and Total Differentiation -- Applications of Partial Differentiation -- Multiple Integration -- Applications and Approximations of Multiple Integrals -- Double Series and Improper Double Integrals En línea: http://dx.doi.org/10.1007/978-1-4419-1621-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33601

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