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Author: M. J. D. Powell
Publisher: Cambridge University Press
ISBN: 9780521295147
Category : Mathematics
Languages : en
Pages : 356
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Book Description
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Author: M. J. D. Powell
Publisher: Cambridge University Press
ISBN: 9780521295147
Category : Mathematics
Languages : en
Pages : 356
Get Book Here
Book Description
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Author: Barry Mazur
Publisher: Cambridge University Press
ISBN: 1107101921
Category : Mathematics
Languages : en
Pages : 155
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Book Description
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Author: Gennaro S. Rodrigues
Publisher: Springer Nature
ISBN: 3031157176
Category : Technology & Engineering
Languages : en
Pages : 137
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Book Description
This book introduces the concept of approximate computing for software and hardware designs and its impact on the reliability of embedded systems. It presents approximate computing methods and proposes approximate fault tolerance techniques applied to programmable hardware and embedded software to provide reliability at low computational costs. The book also presents fault tolerance techniques based on approximate computing, thus presenting how approximate computing can be applied to safety-critical systems.
Author: Nuno Miguel Fonseca Ferreira
Publisher: Springer
ISBN: 9400771835
Category : Technology & Engineering
Languages : en
Pages : 311
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Book Description
This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.
Author: Athanasios C. Antoulas
Publisher: SIAM
ISBN: 0898716586
Category : Mathematics
Languages : en
Pages : 489
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Book Description
Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
Author: Ronald Green
Publisher: John Hunt Publishing
ISBN: 1785356968
Category : Philosophy
Languages : en
Pages : 284
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Book Description
Time seems to flash by when we are enjoying ourselves, and slows to a crawl when we are bored. Why? Does time exist, or is it an illusion? Does it flow? Is it linear? How real are our memories? When is now? These are just some of the questions that Time To Tell asks in its foray into what time is for us, what it does to us and for us, and how we live and react to it in our daily lives. Digging down to the roots of our lived experience in the world, Time To Tell takes us through a journey replete with twists and turns and “aha!” moments. Challenging the obvious, the book asks us to look anew at our perspective of what we naturally take for granted. Rattling the comfort of instant satisfaction, of reality shows, celebrity worship and the self-glorification of the I-generation, Ronald Green, with panache and authority, takes us on a journey that allows us a new way of looking at ourselves in the world, and to act upon what we discover.
Author: Alexander P. Khain
Publisher: Cambridge University Press
ISBN: 1108651550
Category : Science
Languages : en
Pages : 643
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Book Description
This book presents the most comprehensive and systematic description currently available of both classical and novel theories of cloud processes, providing a much-needed link between cloud theory, observation, experimental results, and cloud modeling. This volume shows why and how modern models serve as a major tool of investigation of cloud processes responsible for atmospheric phenomena, including climate change. It systematically describes classical as well as recent advancements in cloud physics, including cloud-aerosol interaction; collisions of particles in turbulent clouds; and the formation of multiphase cloud particles. As the first of its kind to serve as a practical guide for using state-of-the-art numerical cloud models, major emphasis is placed on explaining how microphysical processes are treated in modern numerical cloud resolving models. The book will be a valuable resource for advanced students, researchers and numerical model designers in cloud physics, atmospheric science, meteorology, and environmental science.
Author: W. Gellert
Publisher: Springer Science & Business Media
ISBN: 9401169829
Category : Science
Languages : en
Pages : 833
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Book Description
It is commonplace that in our time sc:iem:e and technology cannot be mastered without the tools of mathematics; but the same applies to an ever growing extent to many domains of everyday life, not least owing to the spread of cybernetic methods and arguments. As a consequence, there is a wide demand for a survey of the results of mathematics. for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over· emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.
Author: Harold Cohen
Publisher: Springer Science & Business Media
ISBN: 1441998365
Category : Mathematics
Languages : en
Pages : 493
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Book Description
This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
