Any suggestions for understanding notation in Tensor Calculus?

In summary, the conversation is about a book that the person has been reading and enjoying, but they have trouble with the notation used. They are looking for suggestions for other resources that focus on tensor notation. Another person suggests reading the first two chapters of an online text, but the original person is unsure if it covers tensor notation. A third person suggests a different resource that specifically addresses tensor notation.
  • #1
Xamien
11
0
I have a book that I've been reading off and on: https://www.amazon.com/dp/012200681X/?tag=pfamazon01-20

It's enjoyable but the only issue I'm having with it is the notation used, still. The book is definitely good at what it wants to achieve, which is a bridging text to the math for tensors, et al. I just wish it had spent more time on the notation being used, with more examples highlighting the notation's use. Does anyone have suggestions for such a purpose?
 
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  • #2
  • #3
That pdf is a fabulous read and I'll be poring over it when I get a chance. A cursory glance revealed nothing on the use of tensor notation, though. Am I not looking deeply enough?
 
  • #4
Perhaps I've missed the point. Tell me what you mean by use of tensor notation.
 

1. What is Tensor Notation?

Tensor notation is a mathematical notation used to express and manipulate tensors, which are mathematical objects that describe the relationships between different quantities. It uses subscripts and superscripts to represent indices, which correspond to the different components of a tensor.

2. What is the significance of Einstein Summation Convention in Tensor Notation?

The Einstein Summation Convention is a convention used in tensor notation to simplify expressions involving summation over repeated indices. According to this convention, any index that appears twice in a single term is implicitly summed over all possible values, unless it is explicitly indicated otherwise.

3. How does Tensor Notation differ from Matrix Notation?

Tensor notation and matrix notation are both used to represent mathematical objects, but they differ in terms of the number of dimensions they can represent. While matrix notation is limited to two dimensions, tensor notation can represent objects of any number of dimensions. Additionally, tensor notation uses index notation to represent components, while matrix notation uses row and column indices.

4. What are some common operations performed using Tensor Notation?

Tensor notation is commonly used for operations such as addition, multiplication, contraction, and differentiation of tensors. It is also used to represent and manipulate equations in various fields such as physics, engineering, and mathematics.

5. How can I learn Tensor Notation?

There are various online resources and textbooks available to learn tensor notation, including video tutorials, interactive courses, and practice problems. It is recommended to have a strong foundation in linear algebra and multivariable calculus before delving into tensor notation.

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