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slave
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02 Jun 2012, 11:47 pm

Aspie_SE10 wrote:
Me :)

BSc Pure Maths
MSc Mathematics and Statistics
PhD Geospatial Statistical Modelling

LOVE my statistics :)


Congratulations on your achievements as well!



Aspie_SE10
Velociraptor
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03 Jun 2012, 11:48 am

slave wrote:
Aspie_SE10 wrote:
Me :)

BSc Pure Maths
MSc Mathematics and Statistics
PhD Geospatial Statistical Modelling

LOVE my statistics :)


Congratulations on your achievements as well!


Thank you!

When I started my PhD I was really looking forward to calling myself "doctor" but when I got it I didn't want to - strange.



slave
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08 Jun 2012, 5:44 pm

Aspie_SE10 wrote:
slave wrote:
Aspie_SE10 wrote:
Me :)

BSc Pure Maths
MSc Mathematics and Statistics
PhD Geospatial Statistical Modelling

LOVE my statistics :)


Congratulations on your achievements as well!


Thank you!

When I started my PhD I was really looking forward to calling myself "doctor" but when I got it I didn't want to - strange.


All the best, Doc! :)



jamieevren1210
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30 Jun 2012, 8:10 am

AstroGeek wrote:
I enjoy math, but I prefer physics.

I enjoy physics, but I prefer math.


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monkeykoder
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30 Jun 2012, 10:18 am

marshall wrote:
AspieRogue wrote:
marshall wrote:


I'm trying to understand the connection between the mathematical definition of tensor and the definition physicists and fluid dynamicists use. I don't think I'm quite there yet. I usually prefer the definitions mathematicians devise in terms of precision and clarity, but they can be lacking in intuitive motivation.

In physics tensors are linear relations between vector quantities that preserve their geometric meaning under different choices of coordinate bases. Physical vectors have the same meaning as first order tensors and higher order tensors are linear geometrically preserving relations between two lower order tensors. My problem is the notation physicists use leads one to confuse the multi-dimensional arrays of numbers that represent tensors with tensors themselves. Tensors are really something more than just indexed multi-dimensional arrays.


You know about linear transformations, right? A linear transformation can qualify as a rank-2 tensor provided that it obeys the requisite transformation rules. Physicists generally work with tensors of rank 2. Tensors of higher rank are generally encountered more frequently in (pure)differential geometry and general relativity.


I guess I'd like to understand precisely how the definition Ruveyn gave is equivalent to the definition used for continuum/fluid mechanics. I'm not sure how stress tensor and strain tensor are linear transformations


I'm not particularly familiar with tensors per-se but I do understand transformations. What little I do understand about tensors says that tensors are a subset of the linear transformations from one frame to another that preserve certain properties. This is just a guess but the understanding of math and physics that I have says that most likely your stress and strain tensors are a mapping from position space to "stress space" the transformation being a description of the "stress" at a given position.