Learning Tensor Calculus: Struggling and Need Help!

In summary, the conversation is about someone trying to learn Tensor Calculus from a book but is stuck and needs to see problems being solved. They ask for suggestions for videos or tutors and someone recommends a book by James Simmonds and suggests looking for MIT videos online. Another person suggests working through problems in D'Inverno's book and shares a link to a helpful PDF about common mistakes when working with tensors.
  • #1
ourstarfish
1
0
I am trying to teach myself Tensor Calculus from a book. I am stuck. Websites and reading don't help. I need to see how the problems are actually done. Does anyone know of any videos or tutors that can help? Tried everything but no luck. At least if you can see a problem worked in class then you know what to do. Any suggestions?
 
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  • #2
I know you said reading hasn't helped, but if you can get hold of the book https://www.amazon.com/dp/354094088X/?tag=pfamazon01-20 by James Simmonds, read it. It is the kind of book a university library is likely to have.

MIT puts videos of some lectures online. You might try googling MIT and tensor analysis.
 
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  • #3
ourstarfish said:
I am trying to teach myself Tensor Calculus from a book. I am stuck. Websites and reading don't help. I need to see how the problems are actually done. Does anyone know of any videos or tutors that can help? Tried everything but no luck. At least if you can see a problem worked in class then you know what to do. Any suggestions?

What's your intended use--area of physics, or just, in general?
 
  • #4
i found that until i saw what the equations meant in 'real' terms, i couldn't get any sort of a grasp on tensor calculus. working through the problems in D'Inverno's 'Introducing Einstein's Relativity' helped me understand.

there was a small pdf i found somewhere on the web about common mistakes that people make when working with tensors. must try and see if i can find it.

http://www.aapt-doorway.org/TGRU/articles/Moore%20GRArticle.pdf" . section 3 and 4. i fell foul of some of the common pitfalls working with tensors myself.
 
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1. What is Tensor Calculus?

Tensor Calculus is a branch of mathematics that deals with the manipulation and analysis of tensors, which are multi-dimensional arrays of numbers. It is used in various fields such as physics, engineering, and computer science to model and solve problems involving multiple variables and dimensions.

2. Why is Tensor Calculus important to learn?

Tensor Calculus is important because it provides a powerful tool for understanding and solving complex problems in various fields. It allows for the representation and manipulation of data in multiple dimensions, making it useful for modeling real-world phenomena. Additionally, many advanced concepts in mathematics and physics rely on tensor calculus, making it essential for further study in these fields.

3. What are some common struggles when learning Tensor Calculus?

Some common struggles when learning Tensor Calculus include understanding the concept of tensors and their different properties, grasping the various operations and transformations that can be performed on tensors, and applying tensor calculus to real-world problems. It also requires a strong foundation in calculus, linear algebra, and vector calculus.

4. How can I improve my understanding of Tensor Calculus?

To improve your understanding of Tensor Calculus, it is essential to have a strong foundation in the prerequisite topics such as calculus, linear algebra, and vector calculus. It is also helpful to practice solving problems and working on applications to gain a better understanding of how tensors are used. Additionally, seeking help from a tutor or joining a study group can also be beneficial.

5. What resources are available for learning Tensor Calculus?

There are various resources available for learning Tensor Calculus, including textbooks, online courses, video lectures, and practice problems. Some recommended textbooks include "Tensor Calculus: A Concise Course" by Ali Taheri and "Introduction to Tensor Calculus, Relativity and Cosmology" by Derek F. Lawden. Online resources such as Khan Academy and MIT OpenCourseWare also offer free courses on Tensor Calculus.

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