Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Complex Analysis written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2011-07-01 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
Download or read book Partial Differential Equations and Complex Analysis written by Steven G. Krantz and published by CRC Press. This book was released on 1992-07-02 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
Download or read book A Course in Advanced Calculus written by Robert S. Borden and published by Courier Corporation. This book was released on 2012-09-11 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This remarkable undergraduate-level text offers a study in calculus that simultaneously unifies the concepts of integration in Euclidean space while at the same time giving students an overview of other areas intimately related to mathematical analysis. The author achieves this ambitious undertaking by shifting easily from one related subject to another. Thus, discussions of topology, linear algebra, and inequalities yield to examinations of innerproduct spaces, Fourier series, and the secret of Pythagoras. Beginning with a look at sets and structures, the text advances to such topics as limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, and more. Carefully chosen problems appear at the end of each chapter, and this new edition features an additional appendix of tips and solutions for selected problems.
Download or read book Advanced Calculus written by Voxman and published by CRC Press. This book was released on 1981-03-01 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts and applied results ofsignificance that serves to bridge the gap between the two- or three-cemester calculus sequence andsenior/graduate level courses in the theory and appplications of ordinary and partial differentialequations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalizedfunctions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, andbrachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensiveproblem sets found throughout the book test the student's understanding of the topics andhelp develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-levelundergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in thistext will increase students' mathematical maturity and prepare them solidly for senior/graduatelevel topics. The wealth of materials in the text allows the instructor to select topics that are ofspecial interest to the student. A two- or three ll?lester calculus sequence is required for successfuluse of this book.
Download or read book An Introduction to Complex Analysis and Geometry written by John P. D'Angelo and published by American Mathematical Soc.. This book was released on 2010 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The first four chapters provide an introduction to complex analysis with many elementary and unusual applications. Chapters 5 to 7 develop the Cauchy theory and include some striking applications to calculus. Chapter 8 glimpses several appealing topics, simultaneously unifying the book and opening the door to further study.
Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Download or read book A Course in Complex Analysis written by Wolfgang Fischer and published by Springer Science & Business Media. This book was released on 2011-10-21 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.
Download or read book Advanced Calculus written by Louis Brand and published by . This book was released on 1955 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
Download or read book Advanced Calculus of Several Variables written by C. H. Edwards and published by Academic Press. This book was released on 2014-05-10 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Calculus written by Patrick Fitzpatrick and published by American Mathematical Soc.. This book was released on 2009 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Advanced Calculus is intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."--pub. desc.
Download or read book A Comprehensive Course in Analysis written by Barry Simon and published by . This book was released on 2015 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis
Download or read book Introduction to Complex Analysis written by H. A. Priestley and published by OUP Oxford. This book was released on 2003-08-28 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.
Download or read book The Calculus of Complex Functions written by William Johnston and published by American Mathematical Society. This book was released on 2022-04-01 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Download or read book Advanced Calculus written by James J. Callahan and published by Springer Science & Business Media. This book was released on 2010-09-09 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Real Calculus written by Kenneth Sielke Miller and published by . This book was released on 2012-06-01 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
