Book contents
- Frontmatter
- Contents
- Preface
- 1 Linear algebra
- 2 Multilinear algebra
- 3 Differentiation on manifolds
- 4 Homotopy and de Rham cohomology
- 5 Elementary homology theory
- 6 Integration on manifolds
- 7 Vector bundles
- 8 Geometric manifolds
- 9 The degree of a smooth map
- Appendix A Mathematical background
- Appendix B The spectral theorem
- Appendix C Orientations and top-dimensional forms
- Appendix D Riemann normal coordinates
- Appendix E Holonomy of an infinitesimal loop
- Appendix F Frobenius' theorem
- Appendix G The topology of electrical circuits
- Appendix H Intrinsic and extrinsic curvature
- References
- Index
Preface
Published online by Cambridge University Press: 05 June 2014
- Frontmatter
- Contents
- Preface
- 1 Linear algebra
- 2 Multilinear algebra
- 3 Differentiation on manifolds
- 4 Homotopy and de Rham cohomology
- 5 Elementary homology theory
- 6 Integration on manifolds
- 7 Vector bundles
- 8 Geometric manifolds
- 9 The degree of a smooth map
- Appendix A Mathematical background
- Appendix B The spectral theorem
- Appendix C Orientations and top-dimensional forms
- Appendix D Riemann normal coordinates
- Appendix E Holonomy of an infinitesimal loop
- Appendix F Frobenius' theorem
- Appendix G The topology of electrical circuits
- Appendix H Intrinsic and extrinsic curvature
- References
- Index
Summary
Q: What's the difference between an argument and a proof? A: An argument will convince a reasonable person, but a proof is needed to convince an unreasonable one.
Anon.Die Mathematiker sind eine Art Franzosen: Redet man zu ihnen, so bersetzen sie es in ihre Sprache, und dann ist es alsbald ganz etwas anderes. (Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.)
Johann Wolfgang von GoetheThis book offers a concise overview of some of the main topics in differential geometry and topology and is suitable for upper-level undergraduates and beginning graduate students in mathematics and the sciences. It evolved from a set of lecture notes on these topics given to senior-year students in physics based on the marvelous little book by Flanders [25], whose stylistic and substantive imprint can be recognized throughout. The other primary sources used are listed in the references.
By intent the book is akin to a whirlwind tour of many mathematical countries, passing many treasures along the way and only stopping to admire a few in detail. Like any good tour, it supplies all the essentials needed for individual exploration after the tour is over. But, unlike many tours, it also provides language instruction. Not surprisingly, most books on differential geometry are written by mathematicians.
- Type
- Chapter
- Information
- Manifolds, Tensors, and FormsAn Introduction for Mathematicians and Physicists, pp. ix - xiiPublisher: Cambridge University PressPrint publication year: 2013