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Matrix and Tensor Calculus_With Applications to Mechanics,Elasticity and Aeronautics 本资源来自于互联网，仅供学习研究之用，不可涉及任何商业用途，请在下载后24小时内删除。 著作权归原作者或出版社所有。未经发贴人conanwj许可，严禁任何人以任何形式转贴本文，违者必究！ 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 本资源免费奉送，共6个可选网络硬盘链接，4.09 MB。 -------------------------------------------------------------------------------------------------------- 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 -------------------------------------------------------------------------------------------------------- [ Last edited by conanwj on 2009-8-13 at 19:25 ] |
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