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Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics
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Authors(Editors):
Aristotle D. Michal
Publisher: Dover
Pub Date: 2008
Pages: 141
ISBN-13: 978-0-486-46246-2
ISBN-IO: 0-486-46246-3
Preface
This volume is based on a series of lectures on matrix calculus and
tensor calculus, and their applications, given under the sponsorship
of the Engineering, Science, and Management War Training (ESMWT)
program, from August 1942 to March 1943. The group taking the
course included a considerable number of outstanding research engineers
and directors of engineering research and development. I am
very grateful to these men who welcomed me and by their interest
in my lectures encouraged me.
The purpose of this book is to give the reader a working knowledge
of the fundamentals of matrix calculus and tensor calculus, which he
may apply to his own field. Mathematicians, physicists, meteorologists,
and electrical en"eers, as well as mechaiucal and aeronautical e"gineers,
will discover principles applicable to their respective fields.
The last group, for instance, will find material on vibrations, aircraft
flutter, elasticity, hydrodynamics, and fluid mechanics. .
The book is divided into two independent parts,_ the first dealing
with the matrix calculus and its applications, the second with the
tensor calculus and its applications. The minimum of mathematical
concepts is presented in the introduction to each part, the more advanced
mathematical ideas being developed as they are needed in
connection with the applications in the later chapters.
The two-part division of the book is primarily due to the fact that
matrix and tensor calculus are essentially two distinct mathematical
studies. The matrix calculus is a purely analytic and algebraic subject,
whereas the tensor calculus is geometric, being connected with
transformations of coordinates and other geometric concepts. A careful
reading of the first chapter in each part of the book will, clarify
the meaning of the word "tensor," which is occasionally misused in
modem scientific and engineering literature.
I wish to acknowledge with gratitude the kind cooperation of the
Douglas Aircraft Company in making available some of its work in
connection with the last part of Chapter 7 on aircraft flutter. It is a
pleasure to thank several of my students, especially Dr. J. E. Lipp
and Messrs. C. H. Putt and Paul Lieber of the Douglas Aircraft
Company, for making available the material worked out by Mr. Lieber
and his research group. I am also very glad to thank the members of
my seminar on applied mathematics at the California Institute for
their helpful suggestions. I wish to make special mention of Dr. C. C.
Lin, who not only took an active part in the seminar but who also
kindly consented. to have his unpublished researches on some dramatic
applications of the tensor calculus to boundary-layer theory in aer.onautics
incorporated. in Chapter 18. This furnishes an application of
the Riemannian tensor calculus described in Chapter 17. I should
like also to thank Dr. W. Z. Chien for his timely help.
I gratefully acknowledge the suggestions of my colleague Prc;Ifessor
Clark B. Millikan concerning ways of making the book more useful
to aeronautical engineers. .
Above all, I am indebted to my distinguished colleague and friend,
Professor Theodore von K8.rm8.n, director of the Guggenheim Graduate
School of Aeronautics at the California Institute, for honoring me by
an invitation to put my lecture notes in book form for publicat,ion in
the GALCIT series. I "ve also the delightful privilege of expressing
my indebtedness to Dr. Karman for his inspiring conversations and
wise counsel on applied mathematics in general and this volume in
particular, and for encouraging me to make contacts with the aircraft
industry on an advanced mathematical level.
I regret that, in order not to delay unduly the publication of this
boQk, I am unable to include some of my more recent unpublished
researches on the applications of the tensor calculus of curved infinite
dimensional spaces to the vibrations of elastic beams and other elastic
media.
CALIFORNIA INsTITUTE OF TECHNOLOGY
OcroBI!lB, 1946
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Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics.Aristotle D. Michal.Dover .2008
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