Introduction To Analysis In Several Variables

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 445 pages
File Size : 42,9 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 : Mariano Giaquinta,Giuseppe Modica
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 49,6 Mb
Release : 2012-08-31
Category : Mathematics
ISBN : 9780817644147

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Mathematical Analysis by Mariano Giaquinta,Giuseppe Modica Pdf

* Embraces a broad range of topics in analysis requiring only a sound knowledge of calculus and the functions of one variable. * Filled with beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index.

Author : L. Hormander
Publisher : Elsevier
Page : 213 pages
File Size : 55,6 Mb
Release : 1973-02-12
Category : Mathematics
ISBN : 9780444105233

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An Introduction to Complex Analysis in Several Variables by L. Hormander Pdf

An Introduction to Complex Analysis in Several Variables

Author : Volker Scheidemann
Publisher : Springer Nature
Page : 239 pages
File Size : 52,6 Mb
Release : 2023
Category : Functions of complex variables
ISBN : 9783031264283

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Introduction to Complex Analysis in Several Variables by Volker Scheidemann Pdf

This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.

Author : Mariano Giaquinta,Giuseppe Modica
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 43,8 Mb
Release : 2010-07-25
Category : Mathematics
ISBN : 9780817646127

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Mathematical Analysis by Mariano Giaquinta,Giuseppe Modica Pdf

This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 247 pages
File Size : 53,9 Mb
Release : 2020-08-11
Category : Education
ISBN : 9781470456689

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Introduction to Analysis in One Variable by Michael E. Taylor Pdf

This is a text for students who have had a three-course calculus sequence and who are ready to explore the logical structure of analysis as the backbone of calculus. It begins with a development of the real numbers, building this system from more basic objects (natural numbers, integers, rational numbers, Cauchy sequences), and it produces basic algebraic and metric properties of the real number line as propositions, rather than axioms. The text also makes use of the complex numbers and incorporates this into the development of differential and integral calculus. For example, it develops the theory of the exponential function for both real and complex arguments, and it makes a geometrical study of the curve (expit) (expit), for real t t, leading to a self-contained development of the trigonometric functions and to a derivation of the Euler identity that is very different from what one typically sees. Further topics include metric spaces, the Stone–Weierstrass theorem, and Fourier series.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210689

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Calculus of Several Variables by Serge Lang Pdf

This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 45,5 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 : Edward Gaughan
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 42,8 Mb
Release : 2009
Category : Mathematical analysis
ISBN : 9780821847879

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Introduction to Analysis by Edward Gaughan Pdf

"The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.

Author : William F. Trench
Publisher : Prentice Hall
Page : 0 pages
File Size : 46,6 Mb
Release : 2003
Category : Applied mathematics
ISBN : 0130457868

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Introduction to Real Analysis by William F. Trench Pdf

Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Author : Steven G. Krantz
Publisher : Springer
Page : 424 pages
File Size : 47,5 Mb
Release : 2017-09-20
Category : Mathematics
ISBN : 9783319632315

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Harmonic and Complex Analysis in Several Variables by Steven G. Krantz Pdf

Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Author : Ernst Hairer,Gerhard Wanner
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 43,6 Mb
Release : 2008-05-30
Category : Mathematics
ISBN : 9780387770369

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Analysis by Its History by Ernst Hairer,Gerhard Wanner Pdf

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

Author : Lars Hörmander
Publisher : Unknown
Page : 213 pages
File Size : 46,6 Mb
Release : 1979
Category : Analytic functions
ISBN : 072042450X

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An Introduction to Complex Analysis in Several Variables by Lars Hörmander Pdf

Author : Leonhard Euler
Publisher : Springer Science & Business Media
Page : 341 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210214

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Introduction to Analysis of the Infinite by Leonhard Euler Pdf

From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Author : Jiri Lebl
Publisher : Lulu.com
Page : 142 pages
File Size : 40,5 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781365095573

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Tasty Bits of Several Complex Variables by Jiri Lebl Pdf

This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.