Vector and tensor calculus for engineers

Ryszard Buczkowski

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ISBN/ISSN:

978-83-01-23103-3

DOI:

https://doi.org/10.53271/2023.086

Wydawnictwo:

Wydawnictwo Naukowe PWN

Rok wydania:

2023

Liczba stron:

240

XML:ISBN/ISSN:

ONIX MARC21

Bibliografia:

Buczkowski, Ryszard. Vector and tensor calculus for engineers. Red. . Warszawa: Wydawnictwo Naukowe PWN, 2023, 240 s. ISBN 978-83-01-23103-3, doi: https://doi.org/10.53271/2023.086

Bibliografia refWorks:

RT Book, Whole

SR Electronic(1)

A1 Buczkowski, R.

T1 Vector and tensor calculus for engineers

PB Wydawnictwo Naukowe PWN

PP Warszawa

YR 2023

SN 978-83-01-23103-3

DOI https://doi.org/10.53271/2023.086

Bibliografia BibTex:

@Book{ 293262, author = "Buczkowski, Ryszard", editor = "", title = "Vector and tensor calculus for engineers", publisher = "Wydawnictwo Naukowe PWN", year = "2023", address = "Warszawa", isbn = "978-83-01-23103-3", doi = "https://doi.org/10.53271/2023.086" }

Bibliografia endNote:

TY - BOOK

AU - Buczkowski, Ryszard

ED -

TI - Vector and tensor calculus for engineers

PB - Wydawnictwo Naukowe PWN

CY - Warszawa

PY - 2023

SN - 978-83-01-23103-3

ER -

DOI - https://doi.org/10.53271/2023.086

Netografia (standard APA):

Buczkowski, Ryszard. Vector and tensor calculus for engineers [baza danych online] Warszawa: Wydawnictwo Naukowe PWN, 2023 [dostęp: 15 07 2024]. Dostęp w Ibuk Libra: https://libra.ibuk.pl/reader/vector-and-tensor-calculus-for-engineers-ryszard-buczkowski-293262. doi: https://doi.org/10.53271/2023.086

Rachunek tensorowy, rachunek wektorowy, vector calculus, tensor calculus

Książka jest tłumaczeniem wydanego w 2020 roku przez PWN podręcznika „Rachunek wektorowy i tensorowy dla inżynierów”. Przedstawia podstawy rachunku wektorowego i tensorowego, praktyczne ich zastosowanie w obliczeniach wybranych zagadni...

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ISBN/ISSN:

978-83-01-23103-3

DOI:

https://doi.org/10.53271/2023.086

Wydawnictwo:

Wydawnictwo Naukowe PWN

Rok wydania:

2023

Liczba stron:

240

XML:ISBN/ISSN:

ONIX MARC21

Introduction6
Chapter 1. Fundamentals of vector and tensor calculus12
Chapter 2. Point motion in curvilinear coordinates76
Chapter 3. Vector calculus – kinematics (plane motion)126
Chapter 4. Vector calculus – kinematics (spherical motion)144
Chapter 5. Tensor calculus – moments of inertia156
Chapter 6. Problems to solve on your own202
Appendix A. Basic concepts of tensor calculus224
Appendix B. Physical components of the first order tensor (vector)232
References234

VECTORANDTENSORCALCULUSFORENGINEERS

Asnotedbytheauthorhimself,hewasfullyconvincedabout

thenoveltyofhiswork.Intheintroduction,heemphasised

itsinﬂuenceontheworksofotherauthors,includingRudolf

Clebsch.Grassmanndeﬁnedtheconceptsofvectorindependence,

vectorspacedimension,exteriorandinteriormultivectormul-

tiplication.Hewastheﬁrsttointroducetheconceptofexterior

product(einausseresProdukt)asvectorproduct

=−

(cf.p.60-64,ed.of1877;symbolsaccordingtotheoriginal

notation).Incontemporaryliterature,antisymmetrictensorprod-

uct,exteriorproductorwedgeproductisrecordeddiferently,

as^=−^=®−®

baa

awhile

b-thisnotationwas

probablyﬁrstusedbyCartanin1922.Itshouldbenoted,howev-

er,thattheauthordidnotusetheword“vector”(German:Vektor)

directly.HeusesthetermofausseresProduktzweierStrecken

(inGermandieStreckeisaline).Theconceptofvectorspace

wasintroducedbetween1918and1820inaseriesofpapersby

theeminentGermanscientistHermannWeyl(1885-1955,PhDat

theUniversityofGöttingenin1908,supervisorDavidHilbert).

Grassmannalsointroducedtheconceptofn-dimensionalspace,

expandeditsgeometry,ﬁrstafneandthenmetricgeometry.He

providedtheconceptsofexterioralgebra,nowadaysreferredto

asGrassmannalgebra.

HermannG.Grassmannwasalsointerestedinphysics.In1845,

hepublishedapaperonelectrodynamics.Hisresultswerecon-

ﬁrmedbyClausiusin1876.In1853,heformulatedthelawsof

activecolourmixing(nowadaysalsoreferredtoasGrassmann’s

laws),whichbecamethebasicsofcolorimetry(conﬁrmedin

theworkbyprof.Prayerof1876).In1860-1862,hewasactive

inlinguisticsanddevelopedaSanskritdictionary(theliterary

languageofAncient,MedievalandEarlyModernIndia)for

Rigveda(theoldestIndo-Aryanpieceofliterature,workedon

byGrassmannin1872-1875).Helovedmusicandcollected

Pomeranianfolksongs.Hebecameacorrespondent-memberof

theGöttingenScientiﬁcSocietyin1871andamemberofthe

AmericanOrientalSocietyin1876.In1876,theUniversityof

Tübingen(theFacultyofPhilosophy)conferredthetitleofdoctor

honoriscausauponhim.

TheﬁnalyearsofGrassmann’slifewereatimeofphysicalsuf-

fering(heusedawheelchair),butalsorecognitionofhisworks.

Despitehislegcondition,hewastransportedtolecturesinthe

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Vector and tensor calculus for engineers

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