Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 0821847910
  • Release Date: 2006
  • Number of pages: 590
  • Author: Patrick Fitzpatrick
  • Publisher: American Mathematical Soc.



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. Special attention has been paid to the motivation for proofs. Selected topics, such as the Picard Existence Theorem for differential equations, have been included in such a way that selections may be made while preserving a fluid presentation of the essential material. Supplemented with numerous exercises, Advanced Calculus is a perfect book for undergraduate students of analysis.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 1577663020
  • Release Date: 2003
  • Number of pages: 622
  • Author: R. Creighton Buck
  • Publisher: Waveland PressInc



Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9814583928
  • Release Date: 2014
  • Number of pages: 580
  • Author: Lynn Harold Loomis
  • Publisher: World Scientific Publishing Company



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.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 144197332X
  • Release Date: 2010-09-09
  • Number of pages: 526
  • Author: James J. Callahan
  • Publisher: Springer Science & Business Media



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.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9780817684129
  • Release Date: 2013-11-10
  • Number of pages: 508
  • Author: Harold M. Edwards
  • Publisher: Springer Science & Business Media



In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature...is that it is fun—it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. —The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. —The American Mathematical Monthly (1994) Based on the Second Edition

Advanced Calculus of Several Variables

  • Filename: advanced-calculus-of-several-variables.
  • ISBN: 9780486131955
  • Release Date: 2012-10-10
  • Number of pages: 480
  • Author: C. H. Edwards
  • Publisher: Courier Corporation



Modern conceptual treatment of multivariable calculus, emphasizing interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. Over 400 well-chosen problems. 1973 edition.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9780486137865
  • Release Date: 2012-10-16
  • Number of pages: 432
  • Author: Avner Friedman
  • Publisher: Courier Corporation



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.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9780486134666
  • Release Date: 2012-05-23
  • Number of pages: 544
  • Author: David V. Widder
  • Publisher: Courier Corporation



Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9781118030677
  • Release Date: 2011-02-14
  • Number of pages: 416
  • Author: Leonard F. Richardson
  • Publisher: John Wiley & Sons



Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis. Following an introduction dedicated to writing proofs, the book is divided into three parts: Part One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals. Part Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics. Part Three is dedicated to multivariable advanced calculus, including inverse and implicit function theorems and Jacobian theorems for multiple integrals. Numerous exercises guide readers through the creation of their own proofs, and they also put newly learned methods into practice. In addition, a "Test Yourself" section at the end of each chapter consists of short questions that reinforce the understanding of basic concepts and theorems. The answers to these questions and other selected exercises can be found at the end of the book along with an appendix that outlines key terms and symbols from set theory. Guiding readers from the study of the topology of the real line to the beginning theorems and concepts of graduate analysis, Advanced Calculus is an ideal text for courses in advanced calculus and introductory analysis at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for engineers, scientists, and mathematicians.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 082476949X
  • Release Date: 1981-03-01
  • Number of pages: 696
  • Author: Voxman
  • Publisher: CRC Press



Introduction to linear algebra and ordinary differential equations; Limits and metric spaces; Continuity, compactness and connectedness; The derivative: theory and elementary applications; A first look at integration; Differentiation of functions of several variables; An introduction to fourier analysis; An introduction to modern integration theory; An introduction to complex integration.

Schaum s Outline of Advanced Calculus Third Edition

  • Filename: schaum-s-outline-of-advanced-calculus-third-edition.
  • ISBN: 0071623671
  • Release Date: 2010-03-12
  • Number of pages: 456
  • Author: Robert Wrede
  • Publisher: McGraw Hill Professional



Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you 1,370 fully solved problems Complete review of all course fundamentals Clear, concise explanations of all Advanced Calculus concepts Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores! Topics include: Numbers; Sequences; Functions, Limits, and Continuity; Derivatives; Integrals; Partial Derivatives; Vectors; Applications of Partial Derivatives; Multiple Integrals; Line Integrals, Surface Integrals, and Integral Theorems; Infinite Series; Improper Integrals; Fourier Series; Fourier Integrals; Gamma and Beta Functions; and Functions of a Complex Variable Schaum's Outlines--Problem Solved.

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9780123846969
  • Release Date: 2010-08-26
  • Number of pages: 256
  • Author: Joseph B. Dence
  • Publisher: Academic Press



Designed for a one-semester advanced calculus course, "Advanced Calculus" explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http: //www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructors Solutions Manual- To come Appropriate rigor for a one-semester advanced calculus course Presents modern materials and nontraditional ways of stating and proving some resultsIncludes precise historical notes throughout the book outstanding feature is the collection of exercises in each chapterProvides coverage of exponential function, and the development of trigonometric functions from the integral

Advanced Calculus

  • Filename: advanced-calculus.
  • ISBN: 9780486173740
  • Release Date: 2013-02-28
  • Number of pages: 560
  • Author: H.K Nickerson
  • Publisher: Courier Corporation



"This book is a radical departure from all previous concepts of advanced calculus," declared the Bulletin of the American Mathematics Society, "and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics." Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives — gradient, divergent, curl, and exterior — are obtained from it by specialization. The corresponding theory of integration is likewise unified, and the various multiple integral theorems of advanced calculus appear as special cases of a general Stokes formula. The text concludes by applying these concepts to analytic functions of complex variables.

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