Introduction To Calculus And Classical Analysis

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Introduction To Calculus And Classical Analysis

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Author : Omar Hijab
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-17

Introduction To Calculus And Classical Analysis written by Omar Hijab and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-17 with Mathematics categories.

This is the second edition of an undergraduate one-variable analysis text. Apart from correcting errors and rewriting several sections, material has been added, notably in Chapter 1 and Chapter 4. A noteworthy addition is a re- variable computation of the radius of convergence of the Bernoulli series using the root test (Chapter 5). What follows is the preface from the ?rst edition. For undergraduate students, the transition from calculus to analysis is often disorienting and mysterious. What happened to the beautiful calculus formulas?Wheredid -? andopensetscomefrom?Itisnotuntillaterthatone integrates these seemingly distinct points of view. When teaching “advanced calculus”, I always had a di?cult time answering these questions. Now,everymathematicianknowsthatanalysisarosenaturallyintheni- teenthcenturyoutofthecalculusoftheprevioustwocenturies.Believingthat it was possible to write a book re?ecting, explicitly, this organic growth, I set outtodoso. I chose several of the jewels of classical eighteenth and nineteenth century analysisandinsertedthemattheendofthebook,insertedtheaxiomsforreals at the beginning, and ?lled in the middle with (and only with) the material necessaryforclarityandlogical completeness.Intheprocess,everylittle piece of one-variable calculus assumed its proper place, and theory and application were interwoven throughout.

Introduction To Calculus And Classical Analysis

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Author : Omar Hijab
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-19

Introduction To Calculus And Classical Analysis written by Omar Hijab and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-19 with Mathematics categories.

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasison computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; There are 385 problems with all the solutions at the back of the text.

Introduction To Calculus And Classical Analysis

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Author : Omar Hijab
language : en
Publisher: Springer
Release Date : 2016-02-09

Introduction To Calculus And Classical Analysis written by Omar Hijab and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-09 with Mathematics categories.

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.

An Introduction To Classical Real Analysis

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Author : Karl R. Stromberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-10

An Introduction To Classical Real Analysis written by Karl R. Stromberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-10 with Mathematics categories.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf

Invitation To Classical Analysis

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Author : Peter Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Invitation To Classical Analysis written by Peter Duren and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Education categories.

This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.

A Concrete Approach To Classical Analysis

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Author : Marian Muresan
language : en
Publisher: Springer Science & Business Media
Release Date : 2015-09-16

A Concrete Approach To Classical Analysis written by Marian Muresan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-16 with Mathematics categories.

Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

Introduction To Calculus And Analysis Ii 1

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Author : Richard Courant
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-14

Introduction To Calculus And Analysis Ii 1 written by Richard Courant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-14 with Mathematics categories.

From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

Introduction To Calculus And Analysis I

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Author : Richard Courant
language : en
Publisher: Springer
Release Date : 1998-12-03

Introduction To Calculus And Analysis I written by Richard Courant and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-03 with Mathematics categories.

From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text.

Calculus And Analysis

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Author : Horst R. Beyer
language : en
Publisher: John Wiley & Sons
Release Date : 2010-04-26

Calculus And Analysis written by Horst R. Beyer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-26 with Mathematics categories.

A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.

A Course In Calculus And Real Analysis

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Author : Sudhir R. Ghorpade
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-05

A Course In Calculus And Real Analysis written by Sudhir R. Ghorpade and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-05 with Mathematics categories.

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.