Prior to the computer era, analytical methods in elasticity had already been developed and - proved up to impressive levels. Relevant mathematical techniques were extensively exploited, contributing signi?cantly to th...
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ISBN:
(数字)9780817644208
ISBN:
(纸本)9780817642723
Prior to the computer era, analytical methods in elasticity had already been developed and - proved up to impressive levels. Relevant mathematical techniques were extensively exploited, contributing signi?cantly to the understanding of physical phenomena. In recent decades, - merical computerized techniques have been re?ned and modernized, and have reached high levels of capabilities, standardization and automation. This trend, accompanied by convenient and high resolution graphical visualization capability, has made analytical methods less attr- tive, and the amount of effort devoted to them has become substantially smaller. Yet, with some tenacity, the tremendous advances in computerized tools have yielded various mature programs for symbolic manipulation. Such tools have revived many abandoned analytical methodologies by easing the tedious effort that was previously required, and by providing additional capab- ities to perform complex derivation processes that were once considered impractical. Generally speaking, it is well recognized that analytical solutions should be applied to re- tively simple problems, while numerical techniques may handle more complex cases. However, it is also agreed that analytical solutions provide better insight and improved understanding of the involved physical phenomena, and enable a clear representation of the role taken by each of the problem parameters. Nowadays, analytical and numerical methods are considered as c- plementary: that is, while analytical methods provide the required understanding,numerical solutions provide accuracy and the capability to deal with cases where the geometry and other characteristics impose relatively complex solutions.
Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hy...
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ISBN:
(数字)9781461553212
ISBN:
(纸本)9780792355595;9781461374282
Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to classical facility location and to problems in computational geometry are pointed out.;The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differen...
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ISBN:
(数字)9783642238994
ISBN:
(纸本)9783642238987
This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computationalmathematics classes. At the same time, the book opens many directions for possible future research.
Das Werk bietet eine Einführung in die wichtigsten mathematischen Grundlagen aus den Gebieten der Linearen und Nichtlinearen Algebra, der analysis und der Diskreten Mathematik für Informatiker. Besondere Sch...
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ISBN:
(数字)9783709133224
Das Werk bietet eine Einführung in die wichtigsten mathematischen Grundlagen aus den Gebieten der Linearen und Nichtlinearen Algebra, der analysis und der Diskreten Mathematik für Informatiker. Besondere Schwerpunkte bilden die in den Computerwissenschaften wichtigen Methoden aus Kombinatorik, Graphentheorie und der Theorie endlicher Körper. Damit zeichnet sich das Werk gegenüber den klassischen Grundlagenwerken der Ingenieurmathematik durch informatikspezifische Inhalte aus. Zahlreiche durchgerechnete Beispiele und Erklärungen sollen die Möglichkeiten des Selbststudiuns fördern. Die Darstellung ist mathematisch exakt und ohne übertriebenen logischen Formalismus. Ziel des Werkes ist es, Studierende der Informatik in mathematischen Einführungsvorlesungen zu unterstützen und Studenten anderer Fächer, die sich in Computermethoden spezialisieren, die spezifischen mathematischen Grundlagen zu vermitteln. Mit Band 3 ist das Werk abgeschlossen.
The dynamics of mechanical rigid-body systems is a highly developed disci pline. The model equations that apply to the tremendous variety of appli cations of rigid-body systems in industrial practice are b...
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ISBN:
(数字)9783662097694
ISBN:
(纸本)9783540022374;9783642056956
The dynamics of mechanical rigid-body systems is a highly developed disci pline. The model equations that apply to the tremendous variety of appli cations of rigid-body systems in industrial practice are based on just a few basic laws of, for example, Newton, Euler, or Lagrange. These basic laws can be written in an extreme compact, symmetrical, and esthetic form, simple enough to be easily learned and kept in mind by students and engineers not only from the area of mechanics, but also from other disciplines like physics, mathematics, or even control, hydraulics, and electronics. This latter aspect is of immense practical importance since mechanisms, machines, robots, and ve hicles in modern industrial practice (sometimes called mechatronic systems) usually include various subsystems from the areas of hydraulics, electronics, pneumatics, and control and are built by engineers which are trained in quite different disciplines. Objectives of this monograph This Volume presents a systematic approach for deriving model equations of many planar and spatial mechanisms: 1. As a first step in DAE form along the systematic approach of Volume I. 2. As a second step in symbolic DE form, as nonlinear and linear state-space equations, andin transfer-function form. The objectives of both the theoretical discussions (Volume I) and the practical applications (this volume) are (see Table 1. 1 of Chapter 1, Volume I): 1. To prepare the reader for efficiently handling and applications of general purpose rigid-body programs to complex mechanisms.
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