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A Course in Calculus and Real Analysis

A Course in Calculus and Real Analysis PDF Author: Sudhir R. Ghorpade
Publisher: Springer Science & Business Media
ISBN: 0387305300
Category : Mathematics
Languages : en
Pages : 442

Book Description
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.

A Course in Calculus and Real Analysis

A Course in Calculus and Real Analysis PDF Author: Sudhir R. Ghorpade
Publisher: Springer Science & Business Media
ISBN: 0387305300
Category : Mathematics
Languages : en
Pages : 442

Book Description
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.

A Course in Multivariable Calculus and Analysis

A Course in Multivariable Calculus and Analysis PDF Author: Sudhir R. Ghorpade
Publisher: Springer Science & Business Media
ISBN: 1441916202
Category : Mathematics
Languages : en
Pages : 486

Book Description
This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. 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. 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.

A First Course in Real Analysis

A First Course in Real Analysis PDF Author: M.H. Protter
Publisher: Springer Science & Business Media
ISBN: 1461599903
Category : Mathematics
Languages : en
Pages : 520

Book Description
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.

A Course In Calculus And Real Analysis

A Course In Calculus And Real Analysis PDF Author: Sudhir Ghorpade
Publisher:
ISBN: 9788181284853
Category : Calculus
Languages : en
Pages : 432

Book Description


A First Course in Real Analysis

A First Course in Real Analysis PDF Author: Sterling K. Berberian
Publisher: Springer Science & Business Media
ISBN: 1441985484
Category : Mathematics
Languages : en
Pages : 249

Book Description
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

A Course in Multivariable Calculus and Analysis

A Course in Multivariable Calculus and Analysis PDF Author: Sudhir R. Ghorpade
Publisher: Springer Science & Business Media
ISBN: 1441916210
Category : Mathematics
Languages : en
Pages : 477

Book Description
This self-contained textbook gives a thorough exposition of multivariable calculus. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. 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. 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.

Basic Real Analysis

Basic Real Analysis PDF Author: James Howland
Publisher: Jones & Bartlett Learning
ISBN: 0763773182
Category : Mathematics
Languages : en
Pages : 233

Book Description
Ideal for the one-semester undergraduate course, Basic Real Analysis is intended for students who have recently completed a traditional calculus course and proves the basic theorems of Single Variable Calculus in a simple and accessible manner. It gradually builds upon key material as to not overwhelm students beginning the course and becomes more rigorous as they progresses. Optional appendices on sets and functions, countable and uncountable sets, and point set topology are included for those instructors who wish include these topics in their course. The author includes hints throughout the text to help students solve challenging problems. An online instructor's solutions manual is also available.

A Course in Real Analysis

A Course in Real Analysis PDF Author: Hugo D. Junghenn
Publisher: CRC Press
ISBN: 148221928X
Category : Mathematics
Languages : en
Pages : 613

Book Description
A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus at the advanced undergraduate level. The book's material has been extensively classroom tested in the author's two-semester undergraduate course on real analysis at The George Washington University.The first part of the text presents the

A First Course in Real Analysis

A First Course in Real Analysis PDF Author: E.R. Suryanarayan
Publisher: Universities Press
ISBN: 9788173714306
Category : Mathematical analysis
Languages : en
Pages : 192

Book Description


A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis

A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis PDF Author: D. J. H. Garling
Publisher: Cambridge University Press
ISBN: 1107311381
Category : Mathematics
Languages : en
Pages :

Book Description
The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.