Graduate Fluids Lesson 01F: Alternating or Permutation Tensor
Graduate Fluid Mechanics Lesson Series - Lesson 01F: Alternating or Permutation Tensor
In this 8.5-minute video, Professor John Cimbala defines and discusses the alternating tensor, also called the repeating or permutation tensor, and its association with the cross product. He shows how to apply the alternating tensor to express the vorticity vector in tensor notation. Finally, he defines the epsilon-delta relation, a fourth-order tensor relationship that comes in handy later in this lesson series.
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A complete list of the videos, the annotated notes for each video, and the Equation Sheet can be found in this Excel file:
https://www.me.psu.edu/cimbala/Cengel...
The YouTube playlist containing all the lessons in this Graduate Fluid Mechanics Lesson Series is found here:
• Graduate Fluid Mechanics Lesson Serie...
These video lessons are intended for use by first-year graduate students taking their first graduate-level course in fluid mechanics. For example, at Penn State our first-semester course is called Foundations of Fluid Mechanics I (ME 521). A second course follows in sequence, typically in the second semester, called Foundations of Fluid Mechanics II. Both of these courses were created by Professor Cimbala. The video lessons and notes closely follow the notes that Professor Cimbala uses when he teaches the course. Except for a few potential notation issues, however, these video lessons may be useful as a free resource at other schools and for anyone wishing to learn about fluid mechanics.
Professor Cimbala has created similar video series for other courses, including (Undergraduate) Fluid Mechanics and Air Pollution. All of his videos are available freely on YouTube. You can see videos of a particular category by going to one of Dr. Cimbala's playlists, listed here in alphabetical order:
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Dr. John M. Cimbala (bio site at https://bio.site/johncimbala) is Professor of Mechanical Engineering at Penn State. He is an educator, textbook author, Christian author, husband, father, and grandfather. He also created and maintains a website for helping people grow in their faith called Christian Faith Grower at https://www.christianfaithgrower.com/ His YouTube channel is at / @johncimbala
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