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s00mb

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- Geometry
- Thread starter s00mb
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In summary, Bruce J. West's books on fractional calculus may be useful for someone interested in applications of differential geometry.

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s00mb

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Physics news on Phys.org

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https://www.amazon.com/dp/0521298873/?tag=pfamazon01-20

discusses various applications of differential geometry in the following branches of physics: thermodynamics, Hamiltonian mechanics, electromagnetism, fluids and (of course) cosmology.

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s00mb

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Looks very promising, thank you!

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Daverz

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Hirani, Anil Nirmal (2003)

Crane, Keenan.

https://www.cs.cmu.edu/~kmcrane/Projects/DDG/

https://www.cs.cmu.edu/~kmcrane/Projects/DDG/paper.pdf

Bossavit, Alain.

https://www.amazon.com/gp/product/0123885604/?tag=pfamazon01-20

related:

https://www.researchgate.net/publication/254470625_On_the_geometry_of_electromagnetism

https://www.researchgate.net/publication/200018385_Differential_Geometry_for_the_student_of_numerical_methods_in_Electromagnetism

https://www.researchgate.net/publication/242462763_Computational_electromagnetism_and_geometry_Building_a_finite-dimensional_Maxwell's_house

The errata for the Burke's book is atDaverz said:

http://www.ucolick.org/~burke/forms/errata.ps

linked from http://www.ucolick.org/~burke/class/adg.html

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s00mb

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- #7

Frabjous

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I do not know if this is still of interest to you

Differential geometry applied to classical mechanics is sometimes known as geometric mechanics.

https://www.amazon.com/dp/0387968903/?tag=pfamazon01-20

https://www.amazon.com/dp/038798643X/?tag=pfamazon01-20

https://www.amazon.com/dp/0821844385/?tag=pfamazon01-20

https://www.amazon.com/dp/0387967907/?tag=pfamazon01-20

https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20

https://www.amazon.com/dp/0199212902/?tag=pfamazon01-20

https://www.amazon.com/dp/184816775X/?tag=pfamazon01-20

https://www.amazon.com/dp/1848167784/?tag=pfamazon01-20

https://www.amazon.com/dp/3319569511/?tag=pfamazon01-20

Control Theory

https://www.amazon.com/dp/1493930168/?tag=pfamazon01-20

Solid Mechanics

https://www.amazon.com/dp/9814616036/?tag=pfamazon01-20

Differential geometry applied to information theory is known as information geometry.

https://www.amazon.com/dp/B01BDF0CQM/?tag=pfamazon01-20

https://math.ucr.edu/home/baez/information/

Bruce J. West has written several books on fractional calculus. I know that he cares about applications.

Differential geometry applied to classical mechanics is sometimes known as geometric mechanics.

https://www.amazon.com/dp/0387968903/?tag=pfamazon01-20

https://www.amazon.com/dp/038798643X/?tag=pfamazon01-20

https://www.amazon.com/dp/0821844385/?tag=pfamazon01-20

https://www.amazon.com/dp/0387967907/?tag=pfamazon01-20

https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20

https://www.amazon.com/dp/0199212902/?tag=pfamazon01-20

https://www.amazon.com/dp/184816775X/?tag=pfamazon01-20

https://www.amazon.com/dp/1848167784/?tag=pfamazon01-20

https://www.amazon.com/dp/3319569511/?tag=pfamazon01-20

Control Theory

https://www.amazon.com/dp/1493930168/?tag=pfamazon01-20

Solid Mechanics

https://www.amazon.com/dp/9814616036/?tag=pfamazon01-20

Differential geometry applied to information theory is known as information geometry.

https://www.amazon.com/dp/B01BDF0CQM/?tag=pfamazon01-20

https://math.ucr.edu/home/baez/information/

Bruce J. West has written several books on fractional calculus. I know that he cares about applications.

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- #8

s00mb

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caz said:

Differential geometry applied to classical mechanics is sometimes known as geometric mechanics.

https://www.amazon.com/dp/0387968903/?tag=pfamazon01-20

https://www.amazon.com/dp/038798643X/?tag=pfamazon01-20

https://www.amazon.com/dp/0821844385/?tag=pfamazon01-20

https://www.amazon.com/dp/0387967907/?tag=pfamazon01-20

https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20

https://www.amazon.com/dp/0199212902/?tag=pfamazon01-20

https://www.amazon.com/dp/184816775X/?tag=pfamazon01-20

https://www.amazon.com/dp/1848167784/?tag=pfamazon01-20

https://www.amazon.com/dp/3319569511/?tag=pfamazon01-20

Control Theory

https://www.amazon.com/dp/1493930168/?tag=pfamazon01-20

Solid Mechanics

https://www.amazon.com/dp/9814616036/?tag=pfamazon01-20

Differential geometry applied to information theory is known as information geometry.

https://www.amazon.com/dp/B01BDF0CQM/?tag=pfamazon01-20

https://math.ucr.edu/home/baez/information/

Bruce J. West has written several books on fractional calculus. I know that he cares about applications.

Yes I am still interested, which one would apply the most of geometric arguments in your opinion(in regard to the dynamics books)? I've seen stuff on information geometry, personally I prefer stochastic geometry over that. I am a little biased though because I have more experience with topics relating to the latter though.

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Frabjous

Gold Member

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s00mb said:Yes I am still interested, which one would apply the most of geometric arguments in your opinion(in regard to the dynamics books)? I've seen stuff on information geometry, personally I prefer stochastic geometry over that. I am a little biased though because I have more experience with topics relating to the latter though.

I’ve gotten interested in advanced mechanics over COVID, so you are seeing a list of interesting things that I have found. I apologize for not having read and absorbed them all so that I can give a good review

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s00mb

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That's no problem, the one about dynamics on manifolds seems to be the one for me to look at. I like manifold theory too, I imagine they'd apply some tensors or Riemann geometry in it.caz said:I’ve gotten interested in advanced mechanics over COVID, so you are seeing a list of interesting things that I have found. I apologize for not having read and absorbed them all so that I can give a good review

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Frabjous

Gold Member

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- #12

dx

Homework Helper

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- #13

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Such as?love_42 said:contains material/approach that is not generally discussed in books on differential geometry

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martinbn

Science Advisor

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Sheaves, exact sequences, cohomology.Demystifier said:Such as?

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dx

Homework Helper

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Demystifier said:Such as?

Have you heard of a 'structure sheaf'?

https://en.wikipedia.org/wiki/Differentiable_manifold#Structure_sheaf

It is a really awesome book.

Differential geometry is a branch of mathematics that studies the properties of curves and surfaces in multi-dimensional spaces. It uses tools from calculus, linear algebra, and topology to understand the geometric properties of these objects.

Differential geometry has many applications in various fields such as physics, engineering, computer graphics, and robotics. It is used to model and analyze the shape and movement of objects in these fields.

Some examples of differential geometry in real life include the design of curved roads and bridges, the analysis of fluid flow in pipes and channels, and the study of the shape of the Earth's surface.

The main concepts in differential geometry include curves, surfaces, manifolds, tangent spaces, curvature, and geodesics. These concepts are used to describe and analyze the properties of geometric objects.

Yes, a strong foundation in calculus, linear algebra, and topology is necessary to fully understand a book on differential geometry. However, there are also introductory texts available that require only basic knowledge of these subjects.

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