A First Course in the Numerical Analysis of Differential Equations


Author: A. Iserles
Publisher: Cambridge University Press
ISBN: 0521734908
Category: Mathematics
Page: 459
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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A First Course in the Numerical Analysis of Differential Equations


Author: Arieh Iserles
Publisher: Cambridge University Press
ISBN: 9780521556552
Category: Mathematics
Page: 378
View: 5049

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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations.

Nonlinear Inverse Problems in Imaging


Author: Jin Keun Seo,Eung Je Woo
Publisher: John Wiley & Sons
ISBN: 1118478150
Category: Technology & Engineering
Page: 376
View: 2972

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This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging

Numerik 3x9

Drei Themengebiete in jeweils neun kurzen Kapiteln
Author: Sören Bartels
Publisher: Springer-Verlag
ISBN: 3662482037
Category: Mathematics
Page: 380
View: 6746

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Dieses Buch bietet eine Einführung in Methoden zur praktischen Lösung mathematischer Probleme, wie der Bestimmung von Eigenwerten, der Approximation und Integration von Funktionen und der näherungsweisen Lösung gewöhnlicher Differenzialgleichungen. Vorausgesetzt werden nur Grundkenntnisse aus der linearen Algebra und Analysis sowie elementare Programmiererfahrungen. Lernziele, Tests zur Selbstüberprüfung und Anwendungsaufgaben am Ende jedes Kapitels vertiefen das Verständnis. Im Anhang des Buchs finden sich unter anderem eine umfangreiche Aufgabensammlung, detaillierte Beschreibungen für Programmierprojekte, Einführungen in die Programmiersprachen Matlab und C und einige Beispielprogramme.

A First Course in Computational Fluid Dynamics


Author: H. Aref,S. Balachandar
Publisher: Cambridge University Press
ISBN: 1107178517
Category: Science
Page: 417
View: 3983

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Fluid mechanics is a branch of classical physics that has a rich tradition in applied mathematics and numerical methods. It is at work virtually everywhere, from nature to technology. This broad and fundamental coverage of computational fluid dynamics (CFD) begins with a presentation of basic numerical methods and flows into a rigorous introduction to the subject. A heavy emphasis is placed on the exploration of fluid mechanical physics through CFD, making this book an ideal text for any new course that simultaneously covers intermediate fluid mechanics and computation. Ample examples, problems and computer exercises are provided to allow students to test their understanding of a variety of numerical methods for solving flow physics problems, including the point-vortex method, numerical methods for hydrodynamic stability analysis, spectral methods and traditional CFD topics.

Numerical Methods for Chemical Engineering

Applications in MATLAB
Author: Kenneth J Beers,Kenneth J. Beers
Publisher: Cambridge University Press
ISBN: 9780521859714
Category: Juvenile Nonfiction
Page: 474
View: 4106

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Applications of numerical mathematics and scientific computing to chemical engineering.

Analysis II


Author: Christiane Tretter
Publisher: Springer-Verlag
ISBN: 3034804768
Category: Mathematics
Page: 149
View: 3686

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Das Lehrbuch ist der zweite von zwei einführenden Bänden in die Analysis. Es zeichnet sich dadurch aus, dass alle Themen der Analysis 2 kompakt zusammengefasst sind und dennoch auf typische Schwierigkeiten eingegangen wird. Beginnend mit der Topologie metrischer Räume über die Differentialrechnung von Funktionen mehrerer reeller Variablen bis zu gewöhnlichen Differentialgleichungen und Fourierreihen, enthält das Buch alle prüfungsrelevanten Inhalte. Der Stoff kann anhand von Beispielen, Gegenbeispielen und Aufgaben nachvollzogen werden.

Essential Mathematical Methods for the Physical Sciences


Author: K. F. Riley,M. P. Hobson
Publisher: Cambridge University Press
ISBN: 1139492942
Category: Science
Page: N.A
View: 9842

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The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over 300 worked examples show how to use the techniques and around 100 self-test questions in the footnotes act as checkpoints to build student confidence. Nearly 400 end-of-chapter problems combine ideas from the chapter to reinforce the concepts. Hints and outline answers to the odd-numbered problems are given at the end of each chapter, with fully-worked solutions to these problems given in the accompanying Student Solutions Manual. Fully-worked solutions to all problems, password-protected for instructors, are available at www.cambridge.org/essential.

Solving ODEs with MATLAB


Author: L. F. Shampine,I. Gladwell,S. Thompson
Publisher: Cambridge University Press
ISBN: 9780521530941
Category: Mathematics
Page: 263
View: 7374

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This book, first published in 2003, provides a concise but sound treatment of ODEs, including IVPs, BVPs, and DDEs.

Mathematics Today

Bulletin of the Institute of Mathematics and Its Applications
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 8896

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Continuum Mechanics

Constitutive Modeling of Structural and Biological Materials
Author: Franco M. Capaldi
Publisher: Cambridge University Press
ISBN: 1107011817
Category: Science
Page: 343
View: 9364

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Designed for continuum mechanics courses and features both the theoretical framework and numerical methods required to model continuous material behaviour.

Sustainable Natural Resource Management

For Scientists and Engineers
Author: Daniel R. Lynch
Publisher: Cambridge University Press
ISBN: 0521899729
Category: Business & Economics
Page: 230
View: 8384

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Natural resources support all human productivity. The sustainable management of natural resources is among the preeminent problems of the current century. Sustainability and the implied professional responsibility start here. This book uses applied mathematics familiar to undergraduate engineers and scientists to examine natural resource management and its role in framing sustainability. Renewable and nonrenewable resources are covered, along with living and sterile resources. Examples and applications are drawn from petroleum, fisheries, and water resources. Each chapter contains problems illustrating the material. Simple programs in commonly available packages (Excel, MATLAB) support the text. The material is a natural prelude to more advanced study in ecology, conservation, and population dynamics, as well as engineering and science. The mathematical description is kept within what an undergraduate student in the sciences or engineering would normally be expected to master for natural systems. The purpose is to allow students to confront natural resource problems early in their preparation.

Computational Gasdynamics


Author: Culbert B. Laney
Publisher: Cambridge University Press
ISBN: 9780521625586
Category: Science
Page: 613
View: 6742

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Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.