|
libcats.org
A Geometric Approach to Differential FormsDavid BachmanThe modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the sophomore undergraduate level. The book begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The author approaches the subject with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. This facilitates the development of differential forms without assuming a background in linear algebra. Throughout the text, emphasis is placed on applications in 3 dimensions, but all definitions are given so as to be easily generalized to higher dimensions. A centerpiece of the text is the generalized Stokes' theorem. Although this theorem implies all of the classical integral theorems of vector calculus, it is far easier for students to both comprehend and remember. The text is designed to support three distinct course tracks: the first as the primary textbook for third semester (multivariable) calculus, suitable for anyone with a year of calculus; the second is aimed at students enrolled in sophomore-level vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, covering more advanced topics such as Maxwell's equations, foliation theory, and cohomology. Containing excellent motivation, numerous illustrations and solutions to selected problems in an appendix, the material has been tested in the classroom along all three potential course tracks. EPUB | FB2 | MOBI | TXT | RTF
* Конвертация файла может нарушить форматирование оригинала. По-возможности скачивайте файл в оригинальном формате.
Популярные книги за неделю:
![]() Сто лет одиночестваАвтор: Маркес Габриэль ГарсияКатегория: Современная проза
Размер книги: 1.46 Mb
![]() Профессиональная разработка в системе 1С Предприятие 8Автор: Габец А.П., Автор: Гончаров Д.И., Автор: Радченко М.Г.(ред.)Категория: Офисные программы бизнес-приложения
Размер книги: 18.19 Mb
![]() Тестирование Дот Ком, или Пособие по жестокому обращению с багами в интернет-стартапахАвтор: Роман Савин
Размер книги: 5.26 Mb
![]() The Fictions of James Joyce and Wyndham Lewis: Monsters of Nature and DesignАвтор: Scott W. KleinКатегория: Наука (общее), Научно-популярное
Размер книги: 4.83 Mb
![]() Materials Science and Engineering An Introduction,9th EditionАвтор: William D. Callister Jr., Автор: David G. Rethwisch
Размер книги: 32.11 Mb
Только что пользователи скачали эти книги:
![]() Излучательные свойства твердых материалов. СправочникАвтор: Шейндлин А.Е. (ред.)
Размер книги: 7.36 Mb
![]() Towards dynamic randomized algorithms in computational geometryАвтор: Monique TeillaudКатегория: Computational geometry
Размер книги: 1.37 Mb
![]() Vector Space Measures and Applications IАвтор: R.M. Aron, Автор: S. DineenКатегория: Lecture notes
Размер книги: 3.14 Mb
![]() Generalized Heisenberg Groups and Damek-Ricci Harmonic SpacesАвтор: Jürgen Berndt, Автор: Franco Tricerri, Автор: Lieven VanheckeКатегория: Lecture notes
Размер книги: 716 Kb
![]() Seminaire de Theorie du Potentiel Paris No 9Автор: Bouleau, Автор: Feyel, Автор: Mokobodzki, Автор: Hirsch.Категория: Lecture notes
Размер книги: 1.29 Mb
![]() Equations over Finite Fields An Elementary ApproachАвтор: W.M. SchmidtКатегория: Lecture notes
Размер книги: 881 Kb
![]() Laser Spectroscopy. V.2 Experimental Techniques (Springer 2008)Автор: Wolfgang DemtröderКатегория: Optics
Размер книги: 11.30 Mb
![]() Introduction to advanced field theoryАвтор: Gabriel BartonКатегория: Quantum field theory
Размер книги: 1.47 Mb
![]() Thirteen Books of Euclid's Elements. Books I-IIАвтор: HeathКатегория: History and Philosophy of Science
Размер книги: 20.11 Mb
|
|