This book presents tensors and differential geometry in a comprehensive
and approachable manner, providing a bridge from the place where physics
and engineering mathematics end, and the place where tensor analysis
begins.
Among the topics examined are tensor analysis, elementary differential
geometry of moving surfaces, and k-differential forms. The book includes
numerous examples with solutions and concrete calculations, which guide
readers through these complex topics step by step. Mindful of the
practical needs of engineers and physicists, book favors simplicity over
a more rigorous, formal approach. The book shows readers how to work
with tensors and differential geometry and how to apply them to modeling
the physical and engineering world.
The authors provide chapter-length treatment of topics at the
intersection of advanced mathematics, and physics and engineering:
- General Basis and Bra-Ket Notation
- Tensor Analysis
- Elementary Differential Geometry
- Differential Forms
- Applications of Tensors and Differential Geometry
- Tensors and Bra-Ket Notation in Quantum Mechanics
The text reviews methods and applications in computational fluid
dynamics; continuum mechanics; electrodynamics in special relativity;
cosmology in the Minkowski four-dimensional space time; and relativistic
and non-relativistic quantum mechanics.
Tensor Analysis and Elementary Differential Geometry for Physicists and
Engineers benefits research scientists and practicing engineers in a
variety of fields, who use tensor analysis and differential geometry in
the context of applied physics, and electrical and mechanical
engineering. It will also interest graduate students in applied physics
and engineering.
