A Geometric Approach to Differential Forms
by David Bachman
Publisher: arXiv 2003
Number of pages: 106
This is a draft of a textbook on differential forms. The primary target audience is sophomore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advanced undergraduate and beginning graduate students. Applications include brief introductions to Maxwell's equations, foliations and contact structures, and DeRham cohomology.
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by J.L. Koszul - Tata Institute of Fundamental Research
From the table of contents: Differential Calculus; Differentiable Bundles; Connections on Principal Bundles; Holonomy Groups; Vector Bundles and Derivation Laws; Holomorphic Connections (Complex vector bundles, Almost complex manifolds, etc.).
by Linfan Mao - InfoQuest
Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, etc.
by R. Bryant, P. Griffiths, D. Grossman - University Of Chicago Press
The authors present the results of their development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms. They also cover certain aspects of the theory of exterior differential systems.
by Ernest Preston Lane - The University Of Chicago Press
Projective Differential Geometry is largely a product of the first three decades of the twentieth century. The theory has been developed in five or more different languages, by three or four well-recognized methods, in various and sundry notations.