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Tensor

Tensor analysis is the generalization of vector analysis. Tensors are a natural extension of vectors and can be used to describe quantities that transform under coordinate changes. Tensor analysis has applications in many areas of physics, including classical mechanics, elasticity, electromagnetism, and Einstein's general theory of relativity. The document discusses the basic definitions of covariant and contravariant tensors as well as symmetric, antisymmetric, and invariant tensors. It also outlines the contents of three chapters covering these tensor types and properties.

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Tina Sagayam
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637 views5 pages

Tensor

Tensor analysis is the generalization of vector analysis. Tensors are a natural extension of vectors and can be used to describe quantities that transform under coordinate changes. Tensor analysis has applications in many areas of physics, including classical mechanics, elasticity, electromagnetism, and Einstein's general theory of relativity. The document discusses the basic definitions of covariant and contravariant tensors as well as symmetric, antisymmetric, and invariant tensors. It also outlines the contents of three chapters covering these tensor types and properties.

Uploaded by

Tina Sagayam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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INTRODUCTION

​Tensor analysis ​is the generalization of vector analysis. The word

tensor were introduced by ​Professor Gregorian Ricci of ​university of padua(Italy)

in 1887 primarily as extension of vector.

The ​tensor analysis​ is a indispensable in a mathematical treatment

of general relativity. A systematic method of investigation the behaviour of

quantities that undergo a co-ordinate transformation is the subject matter of tensor

analysis.

​ Tensors ​are a natural and logical generalization of vectors. It is

well-known that the use of vectors is absolutely essential in mathematical study of

large number of phenomena.

In a similar way ​tensor analysis​ has found applications in various

branches physics. These applications can be broadly divided into two categories

i)applications of nonrelativistic physics


ii)applications in the theory of relativity.

​The ​tensor​ formulation became rather popular when Albert Einstein

used it as a natural tool for the description of his general theory of relativity.

​Tensor analysis​ forms that part of study which is rather suitable

for the mathematical formulation of natural laws respect to underlying frames of

reference.

Chapter 1 deals with general definition of tensor, covariant,


contravariant tensors were discussed.

Chapter 2 ​deals with basic definition and theorem of symmetric,

skew symmetric and invariant tensors.

​Chapter 3 ​deals with the general definition and some theorem

based on the fundamental tensors.


​CONCLUSION

This project​”TENSOR ANALYSIS”​ deals with the basic definition of covariant

and contravariant tensor. It also deals with types of tensors like symmetric,

antisymmetric tensor, invariant tensor and fundamental tensor. Some theorems

were discussed related to the different types of tensors.

The use of tensors in classical physics, special relativity is pointed

out. In case of tensors it is not possible to make any geometrical pictures and hence

tensors have to introduced only through their transformations under changes of the

co-ordinate system.

Tensor analysis applications are used in Riemannian geometry,


mechanics, elasticity, theory of relativity of electromagnetic theory and many other

disciplines of science and engineering​.

​BIBLIOGRAPHY

1. S.​CHAND, H.K.DASS-​“MATHEMATICAL PHYSICS”,


S.Chand & cmn limited.
2. ​P.C.CHATTOPADHDAY​-“MATHEMATICAL
PHYSICS”, New age
International p(ltd) publications, third edition.
3. ​B.D.GUPTA​-“MATHEMATICAL PHYSICS “, Vikas
publishing house pvt.ltd, second edition.
4. ​B.D.GUPTA​-“MATHEMATICAL PHYSICS”, Third revised
edition.
5. ​A.W.JOSHI-​“MATRICES AND TENSORS IN PHYSICS”,
New age international p(ltd) publications, third edition.
6. ​S.L.KAKANI, C.HEMRAJANI​-“MATHEMATICAL
PHYSICS”, CSB publishers & distributions, second edition.
7. ​NAZRUL ISLAM​-“TENSOR AND THEIR
APPLICATIONS”, New age international publications.
8. ​H.C.SINHA AND JOHNWILES AND SONS​-“TENSOR
ANALYSIS”, theory & applications to geometry and
mechanics of continua, second edition.

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