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Advanced Calculus : A Differential Forms Approach / / by Harold M. Edwards



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Autore: Edwards Harold M Visualizza persona
Titolo: Advanced Calculus : A Differential Forms Approach / / by Harold M. Edwards Visualizza cluster
Pubblicazione: Boston, MA : , : Birkhäuser Boston : , : Imprint : Birkhäuser, , 2014
Edizione: 1st ed. 2014.
Descrizione fisica: 1 online resource (XIX, 508 p. 102 illus.) : online resource
Disciplina: 515
Soggetto topico: Mathematical analysis
Analysis (Mathematics)
Functional analysis
Functions of real variables
Sequences (Mathematics)
Analysis
Functional Analysis
Real Functions
Sequences, Series, Summability
Note generali: Originally published: Boston : Houghton Mifflin, c1994.
Includes index.
Nota di contenuto: Constant Forms -- Integrals -- Integration and Differentiation -- Linear Algebra -- Differential Calculus -- Integral Calculus -- Practical Methods of Solution -- Applications -- Further Study of Limits -- Appendices -- Answers to Exercises -- Index.
Sommario/riassunto: 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  .
Titolo autorizzato: Advanced calculus  Visualizza cluster
ISBN: 0-8176-8412-3
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910299974703321
Lo trovi qui: Univ. Federico II
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Serie: Modern Birkhäuser Classics, . 2197-1803