Elements of Numerical Analysis with Mathematica®

Author: John Loustau

Publisher: World Scientific Publishing Company

ISBN: 9813222735

Category: Mathematics

Page: 164

View: 847

Here we present numerical analysis to advanced undergraduate and master degree level grad students. This is to be done in one semester. The programming language is Mathematica. The mathematical foundation and technique is included. The emphasis is geared toward the two major developing areas of applied mathematics, mathematical finance and mathematical biology. Contents: BeginningsLinear Systems and OptimizationInterpolating and FittingNumerical DifferentiationNumerical IntegrationNumerical Ordinary Differential EquationsMonte Carlo Method Readership: Undergraduate and master students.
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Process Modelling and Simulation with Finite Element Methods

Author: William B. J. Zimmerman

Publisher: World Scientific

ISBN: 9789812387936

Category: Mathematics

Page: 382

View: 9104

This book presents a systematic description and case studies of chemical engineering modelling and simulation based on the MATLAB/FEMLAB tools, in support of selected topics in undergraduate and postgraduate programmes that require numerical solution of complex balance equations (ordinary differential equations, partial differential equations, nonlinear equations, integro-differential equations). These systems arise naturally in analysis of transport phenomena, process systems, chemical reactions and chemical thermodynamics, and particle rate processes. Templates are given for modelling both state-of-the-art research topics (e.g. microfluidic networks, film drying, multiphase flow, population balance equations) and case studies of commonplace design calculations -- mixed phase reactor design, heat transfer, flowsheet analysis of unit operations, flash distillations, etc. The great strength of this book is that it makes modelling and simulating in the MATLAB/FEMLAB environment approachable to both the novice and the expert modeller.
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Partielle Differentialgleichungen und numerische Methoden

Author: Stig Larsson,Vidar Thomee

Publisher: Springer-Verlag

ISBN: 3540274227

Category: Mathematics

Page: 272

View: 1755

Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.
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Moving Finite Element Method

Fundamentals and Applications in Chemical Engineering

Author: Maria do Carmo Coimbra,Alirio Egidio Rodrigues,Jaime Duarte Rodrigues,Rui Jorge Mendes Robalo,Rui Manuel Pires Almeida

Publisher: CRC Press

ISBN: 1498723896

Category: Mathematics

Page: 248

View: 6511

This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.
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Elements of Numerical Analysis

Author: Gupta

Publisher: Macmillan

ISBN: 9780230636606

Category:

Page: 624

View: 8746

Elements of Numerical Analysis is intended to serve as a textbook for two-unit (one-year) course in Numerical Analysis at undergraduate or postgraduate level. The topics in the book have been dealt with rigorously and are supported by ample number of solv
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Electrotechnical Systems

Calculation and Analysis with Mathematica and PSpice

Author: Igor Korotyeyev,Valerii Zhuikov,Radoslaw Kasperek

Publisher: CRC Press

ISBN: 9781420087109

Category: Technology & Engineering

Page: 268

View: 6209

Advances in mathematical methods, computer technology, and electrotechnical devices in particular continue to result in the creation of programs that are leading to increased labor productivity. Mathematical and simulation programs—and other programs that unite these two operations—provide the ability to calculate transitional, steady-state processes, stability conditions, and harmonic composition, and are often used to analyze processes in power electronic systems. Electrotechnical Systems: Calculation and Analysis with Mathematica and PSpice explores the potential of two such programs—Mathematica and ORCAD (PSpice)—as they are used for analysis in various areas. The authors discuss the formulation of problems and the steps in their solution. They focus on the analysis of transient, steady-state processes and their stability in non-stationary and nonlinear systems with DC and AC converters. All problems are solved using Mathematica, and program codes are presented. The authors use ORCAD (PSpice) to compare the results obtained by employing Mathematica and to demonstrate the peculiarities associated with its use. This book clearly and concisely illustrates represented expressions, variables, and functions and the general application of the mathematical pocket Mathematica 4.2 for the analysis of the electromagnetic processes in electrotechnical systems. It will be a valuable addition to the library of anyone working with electrotechnical systems.
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The Beauty of Physics: Patterns, Principles, and Perspectives

Author: A. R. P. Rau

Publisher: OUP Oxford

ISBN: 0191019895

Category: Science

Page: 256

View: 2119

The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, there are not even any concrete material particles, only electric and magnetic fields executing simple harmonic motion. But, to a physicist, they are all "just a pendulum". The selection of topics reflects the author's own four-decade career in research physics and his resultant perspective on the subject. While aimed primarily at physicists, including junior students, this book also addresses other readers who are willing to think with symbols and simple algebra in understanding the physical world around us. Each chapter, on themes such as dimensions, transformations, symmetries, or maps, begins with simple examples accessible to all while connecting them later to more sophisticated realizations in more advanced topics of physics.
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Finite-Elemente-Methoden

Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 7391

Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.
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Effective Properties of Heterogeneous Materials

Author: Mark Kachanov,Igor Sevostianov

Publisher: Springer Science & Business Media

ISBN: 9400757158

Category: Science

Page: 389

View: 9227

The book contains state-of the-art reviews in the area of effective properties of heterogeneous materials - the classical field at interface of materials science and solid mechanics. The primary focus is on thermo-mechanical properties, materials science applications, as well as computational aspects and new opportunities provided by rapidly increasing computer powers. The reviews are at the level that is appropriate for a substantial community of researchers working in this field, both at universities and in the industry, and to graduate students. The book can be used as supplementary reading to graduate level courses.
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Nonlinear Mechanics of Thin-Walled Structures

Asymptotics, Direct Approach and Numerical Analysis

Author: Yury Vetyukov

Publisher: Springer Science & Business Media

ISBN: 3709117771

Category: Technology & Engineering

Page: 272

View: 1433

This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book. A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.
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Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations

Author: Collectif,

Publisher: Springer Science & Business Media

ISBN: 9780387945422

Category: Mathematics

Page: 450

View: 7481

This IMA Volume in Mathematics and its Applications MODELING, MESH GENERATION, AND ADAPTIVE NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of the 1993 IMA Summer Program "Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations." We thank Ivo Babuska, Joseph E. Flaherty, William D. Hen­ shaw, John E. Hopcroft, Joseph E. Oliger, and Tayfun Tezduyar for orga­ nizing the workshop and editing the proceedings. We also take this oppor­ tunity to thank those agencies whose financial support made the summer program possible: the National Science Foundation (NSF), the Army Re­ search Office (ARO) the Department of Energy (DOE), the Minnesota Su­ percomputer Institute (MSI), and the Army High Performance Computing Research Center (AHPCRC). A vner Friedman Willard Miller, Jr. xiii PREFACE Mesh generation is one of the most time consuming aspects of com­ putational solutions of problems involving partial differential equations. It is, furthermore, no longer acceptable to compute solutions without proper verification that specified accuracy criteria are being satisfied. Mesh gen­ eration must be related to the solution through computable estimates of discretization errors. Thus, an iterative process of alternate mesh and so­ lution generation evolves in an adaptive manner with the end result that the solution is computed to prescribed specifications in an optimal, or at least efficient, manner. While mesh generation and adaptive strategies are becoming available, major computational challenges remain. One, in particular, involves moving boundaries and interfaces, such as free-surface flows and fluid-structure interactions.
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Numerical analysis

a practical approach

Author: Melvin J. Maron

Publisher: Macmillan College

ISBN: N.A

Category: Mathematics

Page: 534

View: 4560

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Numerical Methods and Applications

5th International Conference, NMA 2002, Borovets, Bulgaria, August 20-24, 2002, Revised Papers

Author: Ivan Dimov,Ivan Lirkov,Svetozar Margenov,Zahari Zlatev

Publisher: Springer Science & Business Media

ISBN: 3540006087

Category: Computers

Page: 574

View: 374

Nuclear magnetic resonance spectroscopy is one of the most important analytical methods available today. This practice-oriented textbook aims at teaching the use of NMR spectra in the elucidation of organic structures. The emphasis of NMR - from Spectra to Structures is on practical rather than on theoretical aspects, which are treated only briefly. The book is intended as a practical guide to today's standard NMR experiments for students and laboratory personnel. A set of thirty-five graded problems reinforces the reader's understanding of how problems of structure elucidation are solved by using NMR.
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Numerical methods

Author: Donald Greenspan,P. Rózsa

Publisher: North-Holland

ISBN: N.A

Category: Mathematics

Page: 378

View: 352

Recent results in the important fields of numerical methods are presented in this volume. The areas covered include linear algebra, nonlinear equations, differential equations and applications.
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Numerische lineare Algebra

Eine konzise Einführung mit MATLAB und Julia

Author: Folkmar Bornemann

Publisher: Springer-Verlag

ISBN: 3658128844

Category: Mathematics

Page: 145

View: 8900

Dieses Buch führt anhand grundlegender Problemstellungen der linearen Algebra in das algorithmisch-numerische Denken ein. Die Beschränkung auf die lineare Algebra sichert dabei eine stärkere thematische Kohärenz als sie sonst in einführenden Vorlesungen zur Numerik zu finden ist. Die Darstellung betont die Zweckmäßigkeit von Matrixpartitionierungen gegenüber einer komponentenweisen Betrachtung, was sich nicht nur in einer übersichtlicheren Notation und kürzeren Algorithmen auszahlt, sondern angesichts moderner Computerarchitekturen auch zu signifikanten Laufzeitgewinnen führt. Die Algorithmen und begleitenden numerischen Beispiele werden in der Programmierumgebung MATLAB angegeben, zusätzlich aber in einem Anhang auch in der zukunftsweisenden, frei zugänglichen Programmiersprache Julia. Das vorliegende Buch eignet sich für eine zweistündige Vorlesung über numerische lineare Algebra ab dem zweiten Semester des Bachelorstudiengangs Mathematik.
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