Mathematical Methods for Mechanics: A Handbook with MATLAB Experiments

ISBN-13: 9783642088773 / Angielski / Miękka / 2010 / 624 str.

Eckart W. Gekeler

Opis

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of handouts to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation."

Recenzje

From the reviews:

"Gekeler (Universität Stuttgart, Germany) offers a quality handbook of advanced mathematical concepts as they apply to mechanics; the level and extent of mathematics presented here is not available in any other mechanics work ... . The volume also covers numerical methods applied to mechanical problems with references to MATLAB code. ... Includes 209 examples and 248 references. Summing Up: Recommended. Graduate students, researchers, and faculty." (J. D. Fehribach, Choice, Vol. 46 (11), July, 2009)

Spis treści

Mathematical Auxiliaries.- Numerical Methods.- Optimization.- Variation and Control.- The Road as Goal.- Mass Points and Rigid Bodies.- Rods and Beams.- Continuum Theory.- Finite Elements.- A Survey on Tensor Calculus.- Case Studies.

Blurb

The interaction between mathematics and mechanics is a never ending source of new developments. Today, challenging problems like space flight, gyroscope motions and tidal currents, can be studied on a laptop, feats that people still in the 1950’s dreamed of accomplishing. The present textbook addresses such problems and moreover, a wide-ranging spectrum of topics from bifurcation theory, optimization and control to rigid-body motion and continuum mechanics of elastic bodies and fluids. It fully encompasses the provision of mathematical tools up to their technical application. Because verifiability is a main element of science and numerical mathematics remain lackluster without demonstrations, a portion of the book is dedicated purely to computations. Due to space limitations the author has transferred this information to his homepage. For each of the covered topics the reader can practice mathematical experiments by using the assortment of Matlab-programs belonging to nearly each chapter. A concise program teaches many technical details in short form and data may be altered ad libitum (learning by doing). The reader will be able to produce each picture or diagram from the book by themselves.

Recent Review of the German edition:
"This book introduces the engineering-oriented reader to all the mathematical tools necessary for solving complex problems in the field of mechanics. The mathematics- oriented reader will find various applications of mathematical and numerical methods for modelling comprehensive mechanical-technical practical problems. Therefore this book will be interesting not only for students of various fields but also for practitioners, development engineers or mathematicians" (Hans Bufler, in: Zentralblatt MATH, 2007, Vol. 1100, Issue 2)