jagomart
digital resources
picture1_Calculus Pdf 170337 | Tensor


 165x       Filetype PDF       File size 0.29 MB       Source: www.ita.uni-heidelberg.de


File: Calculus Pdf 170337 | Tensor
introduction to tensor calculus keesdullemond kasperpeeters c 1991 2023 this booklet contains an explanation about tensor calculus for students of physics andengineeringwithabasicknowledgeoflinearalgebra thefocusliesmainlyon acquiring an understanding of the principles and ...

icon picture PDF Filetype PDF | Posted on 26 Jan 2023 | 2 years ago
Partial capture of text on file.
     Introduction to Tensor Calculus
                 KeesDullemond&KasperPeeters
                              c
                              
1991-2023
                   This booklet contains an explanation about tensor calculus for students of physics
                   andengineeringwithabasicknowledgeoflinearalgebra. Thefocusliesmainlyon
                   acquiring an understanding of the principles and ideas underlying the concept of
                   ‘tensor’. We have not pursued mathematical strictness and pureness, but instead
                                               ´
                   emphasisepracticaluse(foramoremathematicallypureresume,pleaseseethebib-
                   liography). Althoughtensorsareappliedinaverybroadrangeofphysicsandmath-
                   ematics, this booklet focuses on the application in special and general relativity.
                   Weareindebtedtoallpeoplewhoreadearlierversionsofthismanuscriptandgave
                                  ¨
                   useful comments, in particular G. Bauerle (University of Amsterdam) and C. Dulle-
                   mondSr. (University of Nijmegen).
                   The original version of this booklet, in Dutch, appeared on October 28th, 1991. A
                   majorupdatefollowedonSeptember26th,1995. Thisversionisare-typesetEnglish
                   translation made in 2008/2010.
                        c
                   Copyright
1991-2010KeesDullemond&KasperPeeters.
                     1     Theindexnotation                                                                                                                           5
                     2     Bases, co- and contravariant vectors                                                                                                       9
                           2.1      Intuitive approach                   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .        9
                           2.2      Mathematicalapproach . . . . . . . . . . . . . . . . . . . . . . . . . .                                                        11
                     3     Introduction to tensors                                                                                                                  15
                           3.1      Thenewinnerproductandthefirsttensor . . . . . . . . . . . . . . .                                                                15
                           3.2      Creating tensors from vectors . . . . . . . . . . . . . . . . . . . . . . .                                                     17
                     4     Tensors, definitions and properties                                                                                                       21
                           4.1      Definition of a tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                   21
                           4.2      Symmetryandantisymmetry . . . . . . . . . . . . . . . . . . . . . . .                                                           21
                           4.3      Contraction of indices                     .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .      22
                           4.4      Tensors as geometrical objects . . . . . . . . . . . . . . . . . . . . . . .                                                    22
                           4.5      Tensors as operators                    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .      24
                     5     Themetrictensorandthenewinnerproduct                                                                                                     25
                           5.1      Themetricasameasuringrod . . . . . . . . . . . . . . . . . . . . . . .                                                          25
                           5.2      Properties of the metric tensor . . . . . . . . . . . . . . . . . . . . . . .                                                   26
                           5.3      Coversuscontra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                     27
                     6     Tensorcalculus                                                                                                                           29
                           6.1      The‘covariance’ of equations . . . . . . . . . . . . . . . . . . . . . . .                                                      29
                           6.2      Additionoftensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                     30
                           6.3      Tensor products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                   31
                           6.4      First order derivatives: non-covariant version . . . . . . . . . . . . . .                                                      31
                           6.5      Rot, cross-products and the permutation symbol . . . . . . . . . . . .                                                          32
                     7     Covariant derivatives                                                                                                                    35
                           7.1      Vectors in curved coordinates . . . . . . . . . . . . . . . . . . . . . . .                                                     35
                           7.2      Thecovariantderivative of a vector/tensor field . . . . . . . . . . . .                                                          36
                     A Tensorsinspecialrelativity                                                                                                                   39
                     B Geometricalrepresentation                                                                                                                    41
                     C Exercises                                                                                                                                    47
                           C.1 Indexnotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                        47
                           C.2 Co-vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                       49
                           C.3 Introduction to tensors . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                        49
                           C.4 Tensors, general . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                       50
                           C.5 Metrictensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                       51
                           C.6 Tensorcalculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .                                                         51
                                                                                                                                                                      3
                       4
The words contained in this file might help you see if this file matches what you are looking for:

...Introduction to tensor calculus keesdullemond kasperpeeters c this booklet contains an explanation about for students of physics andengineeringwithabasicknowledgeoflinearalgebra thefocusliesmainlyon acquiring understanding the principles and ideas underlying concept we have not pursued mathematical strictness pureness but instead emphasisepracticaluse foramoremathematicallypureresume pleaseseethebib liography althoughtensorsareappliedinaverybroadrangeofphysicsandmath ematics focuses on application in special general relativity weareindebtedtoallpeoplewhoreadearlierversionsofthismanuscriptandgave useful comments particular g bauerle university amsterdam dulle mondsr nijmegen original version dutch appeared october th a majorupdatefollowedonseptemberth thisversionisare typesetenglish translation made copyright theindexnotation bases co contravariant vectors intuitive approach mathematicalapproach tensors thenewinnerproductandthersttensor creating from denitions properties denition symmet...

no reviews yet
Please Login to review.