The Advanced Calculus Of One Variable

Author : Tunc Geveci
Publisher : Springer
Page : 382 pages
File Size : 53,7 Mb
Release : 2016-03-30
Category : Mathematics
ISBN : 9783319278070

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Advanced Calculus of a Single Variable by Tunc Geveci Pdf

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 43,8 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Author : Don R. Lick
Publisher : Unknown
Page : 427 pages
File Size : 42,9 Mb
Release : 1971
Category : Calculo de variaciones
ISBN : 0390557439

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The Advanced Calculus of One Variable by Don R. Lick Pdf

Author : C. H. Edwards
Publisher : Academic Press
Page : 470 pages
File Size : 44,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483268057

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Advanced Calculus of Several Variables by C. H. Edwards Pdf

Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

Author : M. Thamban Nair
Publisher : Springer Nature
Page : 350 pages
File Size : 54,7 Mb
Release : 2022-01-22
Category : Mathematics
ISBN : 9783030886370

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Calculus of One Variable by M. Thamban Nair Pdf

This book is designed to serve as a textbook for courses offered to undergraduate and graduate students enrolled in Mathematics. The first edition of this book was published in 2015. As there is a demand for the next edition, it is quite natural to take note of the several suggestions received from the users of the earlier edition over the past six years. This is the prime motivation for bringing out a revised second edition with a thorough revision of all the chapters. The book provides a clear understanding of the basic concepts of differential and integral calculus starting with the concepts of sequences and series of numbers, and also introduces slightly advanced topics such as sequences and series of functions, power series, and Fourier series which would be of use for other courses in mathematics for science and engineering programs. The salient features of the book are - precise definitions of basic concepts; several examples for understanding the concepts and for illustrating the results; includes proofs of theorems; exercises within the text; a large number of problems at the end of each chapter as home-assignments. The student-friendly approach of the exposition of the book would be of great use not only for students but also for the instructors. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in a mathematics course.

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 445 pages
File Size : 55,5 Mb
Release : 2020-07-27
Category : Education
ISBN : 9781470456696

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Introduction to Analysis in Several Variables: Advanced Calculus by Michael E. Taylor Pdf

This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.

Author : Avner Friedman
Publisher : Courier Corporation
Page : 434 pages
File Size : 44,9 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9780486137865

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Advanced Calculus by Avner Friedman Pdf

Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.

Author : James J. Callahan
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 55,7 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781441973320

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Advanced Calculus by James J. Callahan Pdf

With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.

Author : Devendra Kumar
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
Page : 222 pages
File Size : 44,6 Mb
Release : 2014-06-09
Category : Mathematics
ISBN : 9781783320271

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Advanced Calculus of Several Variables by Devendra Kumar Pdf

ADVANCED CALCULUS OF SEVERAL VARIABLES covers important topics of Transformations and topology on Euclidean in n-space Rn Functions of several variables, Differentiation in Rn, Multiple integrals and Integration in Rn. The topics have been presented in a simple clear and coherent style with a number of examples and exercises. Proofs have been made direct and simple. Unsolved problems just after relevant articles in the form of exercises and typical problems followed by suggestions have been given. This book will help the reader work on the problems of Numerical Analysis, Operations Research, Differential Equations and Engineering applications.

Author : Hans Sagan
Publisher : Houghton Mifflin
Page : 700 pages
File Size : 48,5 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015015686689

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Advanced Calculus by Hans Sagan Pdf

Author : Ellen F. Buck,Robert Creighton Buck
Publisher : Unknown
Page : 622 pages
File Size : 46,6 Mb
Release : 1978
Category : Calculus
ISBN : 0070850763

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Advanced Calculus by Ellen F. Buck,Robert Creighton Buck Pdf

Author : Peter R. Mercer
Publisher : Springer
Page : 419 pages
File Size : 42,8 Mb
Release : 2014-10-17
Category : Mathematics
ISBN : 9781493919260

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More Calculus of a Single Variable by Peter R. Mercer Pdf

This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus — such as the real numbers, differentiation and integration, mean value theorems, the exponential function — are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

Author : G. B. Folland
Publisher : Pearson
Page : 0 pages
File Size : 41,9 Mb
Release : 2002
Category : Calcul infinitésimal
ISBN : 0130652652

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Advanced Calculus by G. B. Folland Pdf

For undergraduate courses in Advanced Calculus and Real Analysis. This text presents a unified view of calculus in which theory and practice reinforce each other. It covers the theory and applications of derivatives (mostly partial), integrals, (mostly multiple or improper), and infinite series (mostly of functions rather than of numbers), at a deeper level than is found in the standard advanced calculus books.

Author : Wendell Fleming
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494617

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Functions of Several Variables by Wendell Fleming Pdf

This new edition, like the first, presents a thorough introduction to differential and integral calculus, including the integration of differential forms on manifolds. However, an additional chapter on elementary topology makes the book more complete as an advanced calculus text, and sections have been added introducing physical applications in thermodynamics, fluid dynamics, and classical rigid body mechanics.

Author : Frederick Shenstone Woods
Publisher : Unknown
Page : 420 pages
File Size : 51,8 Mb
Release : 1926
Category : Calculus
ISBN : UCAL:$B529317

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Advanced Calculus by Frederick Shenstone Woods Pdf