A Geometric Approach to Differential Forms

DO NOT buy the Kindle edition of this book. You will be wasting your money. The mathematical fonts are bitmapped and almost unreadable. Amazon needs to fix this problem. Buy the print edition.

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.

The modern subject of differential forms subsumes classical vector calculus. 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. 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 vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, touching on 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. The modern subject of differential forms subsumes classical vector calculus. 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. 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 vector calculus; while the third targets advanced undergraduates and beginning graduate students in physics or mathematics, touching on 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 "The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a geometric perspective accessible at the advanced undergraduate level. 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. The second edition includes a completely new chapter on differential geometry, as well as other new sections, new exercises and new examples. Additional solutions to selected exercises have also been included. The work is suitable for use as the primary textbook for a sophomore-level class in vector calculus, as well as for more upper-level courses in differential topology and differential geometry."--Publisher's website This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached 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. The book contains excellent motivation, numerous illustrations and solutions to selected problems.