If I want to learn about tensor mathematics - where do I need to start

[mtc1973]

If I want to learn about tensor mathematics - where do I need to start (i.e. what precursory mathematical knowledge will I need) and does anyone have any good site/book recommendations?

thanks

 

[Gear300]

This is what I often recommend --
https://www.amazon.com/dp/048661879X/?tag=pfamazon01-20

If you don't already have any, then you'll need to have some background in linear algebra (and for starting tensors, you'll also need familiarity with calculus in Rⁿ space (multivariable calculus)). This book covers the multivariable calculus, but you'll need to learn linear algebra from some other source.

 

[Rasalhague]

A book I've found helpful is Bowen & Wang's Introduction to Vectors and Tensors. It's in two volumes, both online:

http://repository.tamu.edu/handle/1969.1/2502
http://repository.tamu.edu/handle/1969.1/3609

Besides linear algebra and multivariable calculus, it's useful to have at least some basic abstract algebra to understand the language and notation used in definitions.

 

[mtc1973]

excellent - thanks

 

[CellCoree]

To begin learning about tensor mathematics, it is important to have a strong understanding of linear algebra and multivariable calculus. This includes concepts such as vector spaces, matrices, eigenvalues and eigenvectors, partial derivatives, and gradient vectors. Additionally, a solid background in differential equations and abstract algebra can also be helpful.

There are many resources available for learning about tensor mathematics, including textbooks, online courses, and video lectures. Some recommended textbooks include "Introduction to Tensor Calculus and Continuum Mechanics" by John H. Heinbockel and "Tensor Analysis" by Edward Nelson. Online courses and lectures can be found on platforms such as Coursera, edX, and MIT OpenCourseWare.

It is also beneficial to practice solving problems and working through examples to gain a better understanding of the concepts. Some websites that offer practice problems and tutorials include MathIsFun, Khan Academy, and Brilliant.

Overall, the key to learning tensor mathematics is to have a strong foundation in the necessary mathematical concepts and to practice regularly. With dedication and persistence, anyone can learn about tensor mathematics and its applications in various fields of science and engineering.