A Geometric Approach to Differential Forms - David Bachman - Birkhäuser Trade PB

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“Publisher: Birkhäuser Year: 2006ISBN: 9780817644994Description: Trade Paperback, Fine condition, ...
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Product Identifiers

Publisher
Birkhäuser Boston
ISBN-10
0817644997
ISBN-13
9780817644994
eBay Product ID (ePID)
59022985

Product Key Features

Number of Pages
133 Pages
Publication Name
Geometric Approach to Differential Forms
Language
English
Subject
Geometry / Differential, Functional Analysis, Mathematical Analysis
Publication Year
2006
Type
Textbook
Subject Area
Mathematics
Author
David Bachman
Format
Perfect

Dimensions

Item Height
0.4 in
Item Weight
9.6 Oz
Item Length
9.2 in
Item Width
6.4 in

Additional Product Features

Intended Audience
Trade
LCCN
2006-930548
Reviews
"[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." ---MAA Reviews, From the reviews: "[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." ---MAA Reviews "This book is intended as an elementary introduction to the notion of differential forms, written at an undergraduate level. ? The book certainly has its merits and is very nicely illustrated ? . it should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)." (Frans Cantrijn, Mathematical Reviews, Issue 2007 d), From the reviews: "[The author's] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level." ---MAA Reviews "This book is intended as an elementary introduction to the notion of differential forms, written at an undergraduate level. a? The book certainly has its merits and is very nicely illustrated a? . it should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates)." (Frans Cantrijn, Mathematical Reviews, Issue 2007 d)
Dewey Edition
23
TitleLeading
A
Illustrated
Yes
Dewey Decimal
515/.37
Table Of Content
Preface.- Guide to the Reader.-Multivariable Calculus.- Parameterizations.- Introduction to Forms.- Forms.- Differential Forms.- Differentiation of Forms.- Stokes' Theorem.- Applications.- Manifolds.- Non-linear Forms.- References.- Index.- Solutions.
Synopsis
The 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., This text presents differential forms from a geometric perspective accessible at the 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. The text is designed to support three distinct course tracks, all of which have been classroom tested: third semester (multivariable) calculus, vector calculus, and an advanced undergraduate or beginning graduate topics course for physics or mathematics majors. Contains excellent motivation, numerous illustrations and solutions to selected problems in an appendix., The 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.
LC Classification Number
QA381.B33 2006

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