basic_tools:tensor_calculus
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basic_tools:tensor_calculus [2018/04/13 09:48] bogumilvidovic ↷ Page name changed from basic_tools:tensors to basic_tools:tensor_calculus |
basic_tools:tensor_calculus [2020/04/12 14:42] (current) jakobadmin |
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| - | ====== Tensors ====== | + | ====== Tensor Calculus ====== |
| <tabbox Intuitive> | <tabbox Intuitive> | ||
| - | <note tip> | + | <blockquote>A tensor is a relation between one vector and another. If you start with one vector, such as a force, and mathematically apply it to a tensor, then you get another vector. That vector might be, for example, the stress caused by the force. |
| - | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | + | |
| - | </note> | + | That’s the simplest thing they do. Tensors do other things too; for example, the metric tensor represent the geometry of space. A tensor can represent the energy-momentum density. A tensor can represent a combination of electric and magnetic fields in a way that some of Maxwell’s equations greatly simplify. But the simplest and most basic connection is the vector to vector one. |
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| + | A function relates one number (a “scalar”) to another one. A tensor does that for vectors.<cite>http://qr.ae/TUTNzc</cite></blockquote> | ||
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| <tabbox Concrete> | <tabbox Concrete> | ||
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| - | * [[http://amzn.to/2zqbkeU|A Student's Guide to Vectors and Tensors]] by Fleisch (book) | ||
| - | * [[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters (free) | ||
| + | * [[http://amzn.to/2zqbkeU|A Student's Guide to Vectors and Tensors]] by Fleisch - a nice student-friendly introduction | ||
| + | * [[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters (free) | ||
| + | * A Brief on Tensor Analysis by James Simmonds - a concise but great introductory text. | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
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| <blockquote>Tensor calculus is a technique that can be regarded as a follow-up on linear algebra. | <blockquote>Tensor calculus is a technique that can be regarded as a follow-up on linear algebra. | ||
| - | It is a generalisation of classical linear algebra. In classical linear algebra one deals | + | It is a generalization of classical linear algebra. In classical linear algebra one deals |
| - | with vectors and matrices. Tensors are generalisations of vectors and matrices. | + | with vectors and matrices. Tensors are generalizations of vectors and matrices. |
| <cite>[[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters</cite></blockquote> | <cite>[[http://maths.dur.ac.uk/users/kasper.peeters/pdf/tensor_en.pdf|Introduction to Tensor Calculus]] by Kees Dullemond & Kasper Peeters</cite></blockquote> | ||
basic_tools/tensor_calculus.1523605694.txt.gz · Last modified: 2018/04/13 07:48 (external edit)
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