Elements of Numerical Analysis with Mathematica®

Author: John Loustau

Publisher: World Scientific Publishing Company

ISBN: 9813222735

Category: Mathematics

Page: 164

View: 2965

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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Elements of Numerical Analysis

Author: Gupta

Publisher: Macmillan

ISBN: 9780230636606

Category:

Page: 624

View: 7399

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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Applied Numerical Analysis with Mathematica

Author: RENATO M COTTA,LEONARDO S DE B ALVES,MIKHAIL D. MIKHAILOV

Publisher: Editora E-papers

ISBN: 858792222X

Category:

Page: 176

View: 4179

The first notebook (ANA0) aims to introduce the reader to the Mathematica system, illustrating the concepts and commands that will be required in the basic understanding of the notebooks to follow. The second notebook (ANA1) intends to discuss the questions of precision and accuracy in scientific computation, and how the system deals with fixed and variable precision arithmetic. The next eight notebooks (ANA2 through ANA9) deal with the most common computational tasks in numerical analysis, starting with polynomial interpolation and up to the solution of boundary value problems. The next two notebooks (ANA10 and ANA11) include research work by the authors on the use of the Integral Transform Method in the solution of differential eigenvalue problems and nonlinear partial differential equations, respectively.
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Numerical Solution of Partial Differential Equations by the Finite Element Method

Author: Claes Johnson

Publisher: Courier Corporation

ISBN: 0486131599

Category: Mathematics

Page: 288

View: 359

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
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The Mathematical Theory of Finite Element Methods

Author: Susanne C Brenner,L. Ridgway Scott

Publisher: Springer Science & Business Media

ISBN: 1475736584

Category: Mathematics

Page: 363

View: 2225

A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
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An Engineer's Guide to Mathematica

Author: Edward B. Magrab

Publisher: John Wiley & Sons

ISBN: 1118821254

Category: Technology & Engineering

Page: 456

View: 4577

Free Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab Updated material includes: - Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia - Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape - Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements An Engineer's Guide to Mathematica enables the reader to attain the skills to create Mathematica 9 programs that solve a wide range of engineering problems and that display the results with annotated graphics. This book can be used to learn Mathematica, as a companion to engineering texts, and also as a reference for obtaining numerical and symbolic solutions to a wide range of engineering topics. The material is presented in an engineering context and the creation of interactive graphics is emphasized. The first part of the book introduces Mathematica's syntax and commands useful in solving engineering problems. Tables are used extensively to illustrate families of commands and the effects that different options have on their output. From these tables, one can easily determine which options will satisfy one's current needs. The order of the material is introduced so that the engineering applicability of the examples increases as one progresses through the chapters. The second part of the book obtains solutions to representative classes of problems in a wide range of engineering specialties. Here, the majority of the solutions are presented as interactive graphics so that the results can be explored parametrically. Key features: Material is based on Mathematica 9 Presents over 85 examples on a wide range of engineering topics, including vibrations, controls, fluids, heat transfer, structures, statistics, engineering mathematics, and optimization Each chapter contains a summary table of the Mathematica commands used for ease of reference Includes a table of applications summarizing all of the engineering examples presented. Accompanied by a website containing Mathematica notebooks of all the numbered examples An Engineer's Guide to Mathematica is a must-have reference for practitioners, and graduate and undergraduate students who want to learn how to solve engineering problems with Mathematica.
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Computer simulations with Mathematica

explorations in complex physical and biological systems

Author: Richard J. Gaylord,Paul R. Wellin

Publisher: Springer

ISBN: 9780387942742

Category: Computers

Page: 297

View: 7577

The study of natural phenomena using computer simulation is a major new research tool in the physical, chemical, biological and social sciences. It is useful for studying simple systems, and it is essential for the study of complex systems. Using Mathematica, an integrated software environment for scientific programming, numerical analysis and visualization, this book describes computer simulations applicable to a wide range of phenomena.
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Advanced Topics in Finite Element Analysis of Structures

With Mathematica and MATLAB Computations

Author: M. Asghar Bhatti

Publisher: Wiley

ISBN: 9780471648079

Category: Mathematics

Page: 608

View: 1610

Starting from governing differential equations, a unique and consistently weighted residual approach is used to present advanced topics in finite element analysis of structures, such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book features a hands-on approach to understanding advanced concepts of the finite element method (FEM) through integrated Mathematica and MATLAB® exercises.
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Partial Differential Equations

Analytical and Numerical Methods, Second Edition

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898719356

Category: Mathematics

Page: 654

View: 3509

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.
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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: 8168

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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Numerical Analysis with Algorithms and Programming

Author: Santanu Saha Ray

Publisher: CRC Press

ISBN: 1498741762

Category: Mathematics

Page: 685

View: 8132

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.
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The Mathematica Handbook

Author: Martha L Abell,James P. Braselton

Publisher: Academic Press

ISBN: 1483259900

Category: Mathematics

Page: 816

View: 8112

The Mathematica Handbook provides all the Mathematica commands and objects along with typical examples of them. This handbook is intended as a reference of all built-in Mathematica Version 2.0 objects to both beginning and advanced users of Mathematica. The book contains commands and examples of those commands found in the packages of Mathematica, a system for doing mathematics on a computer. The Preface describes how to use the entries of The Handbook and then briefly discusses elementary rules of Mathematica syntax, defining functions, and using commands that are contained in the standard Mathematica packages. Subsequent chapters provide commands for calculations in Calculus, Statistics, and Numerical Math. The commands in these sections are listed within each package, and the packages are listed alphabetically within each folder (or directory) as well. The book will be of use to engineers, computer scientists, physical scientists, mathematicians, business professionals, and students.
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Exploring Calculus

Labs and Projects with Mathematica

Author: Crista Arangala,Karen A. Yokley

Publisher: CRC Press

ISBN: 1498771068

Category: Mathematics

Page: 172

View: 3204

This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.
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Numerical Methods for Ordinary Differential Equations

Author: J. C. Butcher

Publisher: John Wiley & Sons

ISBN: 1119121523

Category: Mathematics

Page: 544

View: 561

A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
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Modelling Metabolism with Mathematica

Author: Peter Mulquiney,Philip W. Kuchel

Publisher: CRC Press

ISBN: 0203503937

Category: Science

Page: 328

View: 9288

With the advent of sophisticated general programming environments like Mathematica, the task of developing new models of metabolism and visualizing their responses has become accessible to students of biochemistry and the life sciences in general. Modelling Metabolism with Mathematica presents the approaches, methods, tools, and algorithms for modelling the chemical-dynamics of metabolic pathways. The authors explain the concepts underpinning the deterministic theory of chemical and enzyme kinetics, present a graded series of computer models of metabolic pathways leading up to that of the human erythrocyte, and document a consistent set of rate equations and associated kinetic parameters. The experimental and theoretical study of metabolism in mammalian cells has a long and fruitful history, but our understanding of cellular metabolism at the molecular level is far from complete. This book enables its readers to formulate their own models of time-dependent metabolic systems and aids them in the quest for the many fundamental and clinically relevant discoveries that remain to be made.
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C Programming and Numerical Analysis

An Introduction

Author: Seiichi Nomura

Publisher: Morgan & Claypool Publishers

ISBN: 1681733366

Category: Technology & Engineering

Page: 198

View: 1413

This book is aimed at those in engineering/scientific fields who have never learned programming before but are eager to master the C language quickly so as to immediately apply it to problem solving in numerical analysis. The book skips unnecessary formality but explains all the important aspects of C essential for numerical analysis. Topics covered in numerical analysis include single and simultaneous equations, differential equations, numerical integration, and simulations by random numbers. In the Appendices, quick tutorials for gnuplot, Octave/MATLAB, and FORTRAN for C users are provided.
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Mathematica for Calculus-Based Physics

Author: Marvin L. De Jong

Publisher: Addison-Wesley

ISBN: 9780201603392

Category: Science

Page: 257

View: 1740

This workbook/laboratory manual, designed for the first- or second-year physics student, integrates a computer algebra system, Mathematica, with calculus-based physics. Students learn physics, mathematics, and Mathematica by applying the system to numerous physics problems drawn from a broad range of topics in introductory calculus-based physics. Mathematica's extensive use of graphs helps students visualize solutions as well as find analytical solutions to the problems, which often are skills needed in physics research.
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Mathematica by Example

Author: Martha L. Abell,James P. Braselton

Publisher: Academic Press

ISBN: 0128124822

Category: Mathematics

Page: 574

View: 8376

Mathematica by Example, Fifth Edition is an essential desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the dramatic changes to functionality and visualization capabilities in the most recent version of Mathematica (10.4). It accommodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers and aspiring programmers seeking further understanding of Mathematica. Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications. Provides a clear organization, integrated topic coverage, and accessible exposition for novices Includes step-by-step instructions for the most popular implementations Contains new applications, exercises and examples from a variety of fields, including biology, physics and engineering Supported by a website providing Mathematica code derived from examples in the book
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Applied Numerical Analysis with Mathematica

Author: RENATO M COTTA,LEONARDO S DE B ALVES,MIKHAIL D. MIKHAILOV

Publisher: Editora E-papers

ISBN: 858792222X

Category:

Page: 176

View: 8405

The first notebook (ANA0) aims to introduce the reader to the Mathematica system, illustrating the concepts and commands that will be required in the basic understanding of the notebooks to follow. The second notebook (ANA1) intends to discuss the questions of precision and accuracy in scientific computation, and how the system deals with fixed and variable precision arithmetic. The next eight notebooks (ANA2 through ANA9) deal with the most common computational tasks in numerical analysis, starting with polynomial interpolation and up to the solution of boundary value problems. The next two notebooks (ANA10 and ANA11) include research work by the authors on the use of the Integral Transform Method in the solution of differential eigenvalue problems and nonlinear partial differential equations, respectively.
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Computational Financial Mathematics using MATHEMATICA®

Optimal Trading in Stocks and Options

Author: Srdjan Stojanovic

Publisher: Springer Science & Business Media

ISBN: 1461200431

Category: Business & Economics

Page: 481

View: 5253

Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions. This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book. Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors.
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