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A Geometric Approach to Differential Forms

  • David Bachman

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David Bachman
    Pages 1-6
  3. David Bachman
    Pages 7-23
  4. David Bachman
    Pages 25-40
  5. David Bachman
    Pages 41-69
  6. David Bachman
    Pages 71-82
  7. David Bachman
    Pages 83-100
  8. David Bachman
    Pages 101-117
  9. David Bachman
    Pages 119-136
  10. Back Matter
    Pages 137-156

About this book

Introduction

"[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 (Review of First Edition)

"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)."                                                                                   —Mathematical Reviews (Review of First Edition)

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.

Keywords

Maxwell's equations Stokes' Theorem differential forms nonlinear forms parameterized curves vector calculus

Authors and affiliations

  • David Bachman
    • 1
  1. 1., Department of MathematicsPitzer CollegeClaremontUSA

Bibliographic information