e mërkurë, 26 shtator 2007

Differential Geometry and Physics

These notes were developed as a supplement to a course on Differential Geometry at the advanced
undergraduate, first year graduate level, which by the author has taught for several years. There
are many excellent good texts in Differential Geometry but very few have an early introduction to
differential forms and their applications to Physics. It is the purpose of these notes to bridge some
of these gaps and thus help the student get a more profound understanding of the concepts involved.
When appropriate, the notes also correlate classical equations to the more elegant but less intuitive
modern formulation of the subject.
These notes should be accessible to students who have completed a traditional training in Advanced
Calculus, Linear Algebra, and differential Equations. Students who master the entirety of
this material will have gained enough background to begin a formal study of the General Theory of
Dr. Gabriel Lugo
Mathematical Sciences
Wilmington, NC 28403

1 Vectors and Curves
1.1 Tangent Vectors .
1.2 Curves in R 3

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