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How do you draw a straight line? How do you determine if a circle is really round? These may sound like simple or even trivial mathematical problems, but to an engineer the answers can mean the difference between success and failure. How Round Is Your Circle? invites readers to explore many of the same fundamental questions that working engineers deal with every day--it's challenging, hands-on, and fun. John Bryant and Chris Sangwin illustrate how physical models are created from abstract mathematical ones. Using elementary geometry and trigonometry, they guide readers through paper-and-pencil reconstructions of mathematical problems and show them how to construct actual physical models themselves--directions included. It's an effective and entertaining way to explain how applied mathematics and engineering work together to solve problems, everything from keeping a piston aligned in its cylinder to ensuring that automotive driveshafts rotate smoothly. Intriguingly, checking the roundness of a manufactured object is trickier than one might think. When does the width of a saw blade affect an engineer's calculations--or, for that matter, the width of a physical line? When does a measurement need to be exact and when will an approximation suffice? Bryant and Sangwin tackle questions like these and enliven their discussions with many fascinating highlights from engineering history. Generously illustrated, How Round Is Your Circle? reveals some of the hidden complexities in everyday things.

Engineering mathematics. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Engineering --- Engineering analysis --- Mathematics

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This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dynamics, and other fields of science and engineering using the general continuum mechanics theory.

Continuum mechanics. --- Engineering mathematics. --- Milieux continus, Mécanique des --- Mathématiques de l'ingénieur --- Milieux continus, Mécanique des --- Mathématiques de l'ingénieur --- Engineering --- Engineering analysis --- Mathematical analysis --- Mechanics of continua --- Elasticity --- Mechanics, Analytic --- Field theory (Physics) --- Mathematics

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This is a sequel to the book “Programming the Boundary Element Method” by G. Beer published by Wiley in 2001. The scope of this book is different however and this is reflected in the title. Whereas the previous book concentrated on explaining the implementation of a limited range of problems into computer code and the emphasis was on programming, in the current book the problems covered are extended, the emphasis is on explaining the theory and computer code is not presented for all topics. The new topics covered range from dynamics to piezo-electricity. However, the main idea, to provide an explanation of the Boundary Element Method (BEM), that is easy for engineers and scientists to follow, is retained. This is achieved by explaining some aspects of the method in an engineering rather than mathematical way. Another new feature of the book is that it deals with the implementation of the method on parallel processing hardware. I. M. Smith, who has been involved in programming the finite element method for decades, illustrates that the BEM is “embarrassingly parallelisable”. It is shown that the conversion of the BEM programs to run efficiently on parallel processing hardware is not too difficult and the results are very impressive, such as solving a 20 000 element problem during a “coffee break”.

Boundary element methods. --- Boundary element methods --- Computer programming. --- FORTRAN (Computer program language) --- Data processing. --- Formula Translation (Computer program language) --- Programming languages (Electronic computers) --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Programming --- Engineering mathematics. --- Engineering. --- Mathematical and Computational Engineering. --- Engineering, general. --- Construction --- Industrial arts --- Technology --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Applied mathematics.

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Among numerical methods applied in acoustics, the Finite Element Method (FEM) is normally favored for interior problems whereas the Boundary Element Method (BEM) is quite popular for exterior ones. That is why this valuable reference provides a complete survey of methods for computational acoustics, namely FEM and BEM. It demonstrates that both methods can be effectively used in the complementary cases. The chapters by well-known authors are evenly balanced: 10 chapters on FEM and 10 on BEM. An initial conceptual chapter describes the derivation of the wave equation and supplies a unified approach to FEM and BEM for the harmonic case. A categorization of the remaining chapters and a personal outlook complete this introduction. In what follows, both FEM and BEM are discussed in the context of very different problems. Firstly, this comprises numerical issues, e.g. convergence, multi-frequency solutions and highly efficient methods; and secondly, solutions techniques for the particular difficulties that arise with external problems, e.g. discussion of absorbing boundaries for FEM and treatment of the non-uniqueness problem for BEM. Finally, both parts on FEM and on BEM are completed by chapters on related problems, e.g. formulations for fluid-structure interaction. In addition to time-harmonic problems, transient problems are considered in some chapters. Many theoretical and industrial applications are presented. Overall, this book is a unified review of the state-of-the-art on FEM and BEM for computational acoustics.

Finite element method. --- Boundary element methods. --- Noise control. --- Fluid dynamics --- Data processing. --- CFD (Computational fluid dynamics) --- Noise prevention --- Acoustical engineering --- Environmental engineering --- Noise --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Isogeometric analysis --- Computer simulation --- Data processing --- Acoustics. --- Engineering. --- Mathematics. --- Computational Intelligence. --- Numerical and Computational Physics, Simulation. --- Applications of Mathematics. --- Math --- Science --- Construction --- Industrial arts --- Technology --- Computational intelligence. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematics

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The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of meetings held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. Topics include theoretical aspects of new numerical techniques and algorithms as well as of applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.

Differential equations --- Numerical analysis --- 517.91 Differential equations --- Mathematics. --- Computer science --- Computer science. --- Applications of Mathematics. --- Computational Mathematics and Numerical Analysis. --- Computational Science and Engineering. --- Informatics --- Science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Math --- Mathematics --- Applied mathematics. --- Engineering mathematics. --- Computer mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis