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Elements of Numerical Analysis

Author : Radhey S. Gupta

Publisher : Cambridge University Press

Page : 778 pages

File Size : 50,59 MB

Release : 2015-05-14

Category : Mathematics

ISBN : 1316338290

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Book Description

Numerical analysis deals with the manipulation of numbers to solve a particular problem. This book discusses in detail the creation, analysis and implementation of algorithms to solve the problems of continuous mathematics. An input is provided in the form of numerical data or it is generated as required by the system to solve a mathematical problem. Subsequently, this input is processed through arithmetic operations together with logical operations in a systematic manner and an output is produced in the form of numbers. Covering the fundamentals of numerical analysis and its applications in one volume, this book offers detailed discussion on relevant topics including difference equations, Fourier series, discrete Fourier transforms and finite element methods. In addition, the important concepts of integral equations, Chebyshev Approximation and Eigen Values of Symmetric Matrices are elaborated upon in separate chapters. The book will serve as a suitable textbook for undergraduate students in science and engineering.



Elements of Numerical Analysis with Mathematica

Author : John Loustau

Publisher : World Scientific Publishing Company

Page : 151 pages

File Size : 31,59 MB

Release : 2017-08-24

Category : Mathematics

ISBN : 9789813222717

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Book Description

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.



The Mathematical Theory of Finite Element Methods

Author : Susanne Brenner

Publisher : Springer Science & Business Media

Page : 369 pages

File Size : 31,22 MB

Release : 2013-03-14

Category : Mathematics

ISBN : 1475736584

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Book Description

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



Numerical Solution of Partial Differential Equations by the Finite Element Method

Author : Claes Johnson

Publisher : Courier Corporation

Page : 290 pages

File Size : 11,11 MB

Release : 2012-05-23

Category : Mathematics

ISBN : 0486131599

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Book Description

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.



Elements of Statistical Computing

Author : R.A. Thisted

Publisher : Routledge

Page : 456 pages

File Size : 38,15 MB

Release : 2017-10-19

Category : Mathematics

ISBN : 1351452746

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Book Description

Statistics and computing share many close relationships. Computing now permeates every aspect of statistics, from pure description to the development of statistical theory. At the same time, the computational methods used in statistical work span much of computer science. Elements of Statistical Computing covers the broad usage of computing in statistics. It provides a comprehensive account of the most important computational statistics. Included are discussions of numerical analysis, numerical integration, and smoothing. The author give special attention to floating point standards and numerical analysis; iterative methods for both linear and nonlinear equation, such as Gauss-Seidel method and successive over-relaxation; and computational methods for missing data, such as the EM algorithm. Also covered are new areas of interest, such as the Kalman filter, projection-pursuit methods, density estimation, and other computer-intensive techniques.



Numerical Approximation Methods for Elliptic Boundary Value Problems

Author : Olaf Steinbach

Publisher : Springer Science & Business Media

Page : 392 pages

File Size : 16,21 MB

Release : 2007-12-22

Category : Mathematics

ISBN : 0387688056

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Book Description

This book presents a unified theory of the Finite Element Method and the Boundary Element Method for a numerical solution of second order elliptic boundary value problems. This includes the solvability, stability, and error analysis as well as efficient methods to solve the resulting linear systems. Applications are the potential equation, the system of linear elastostatics and the Stokes system. While there are textbooks on the finite element method, this is one of the first books on Theory of Boundary Element Methods. It is suitable for self study and exercises are included.



Elements of Numerical Mathematical Economics with Excel

Author : Giovanni Romeo

Publisher : Academic Press

Page : 818 pages

File Size : 43,40 MB

Release : 2019-11-28

Category : Business & Economics

ISBN : 0128176490

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Book Description

Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization shows readers how to apply static and dynamic optimization theory in an easy and practical manner, without requiring the mastery of specific programming languages that are often difficult and expensive to learn. Featuring user-friendly numerical discrete calculations developed within the Excel worksheets, the book includes key examples and economic applications solved step-by-step and then replicated in Excel. After introducing the fundamental tools of mathematical economics, the book explores the classical static optimization theory of linear and nonlinear programming, applying the core concepts of microeconomics and some portfolio theory. This provides a background for the more challenging worksheet applications of the dynamic optimization theory. The book also covers special complementary topics such as inventory modelling, data analysis for business and economics, and the essential elements of Monte Carlo analysis. Practical and accessible, Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization increases the computing power of economists worldwide. This book is accompanied by a companion website that includes Excel examples presented in the book, exercises, and other supplementary materials that will further assist in understanding this useful framework. - Explains how Excel provides a practical numerical approach to optimization theory and analytics - Increases access to the economic applications of this universally-available, relatively simple software program - Encourages readers to go to the core of theoretical continuous calculations and learn more about optimization processes



An Introduction to Numerical Methods and Analysis

Author : James F. Epperson

Publisher : John Wiley & Sons

Page : 579 pages

File Size : 12,47 MB

Release : 2013-06-06

Category : Mathematics

ISBN : 1118626230

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Book Description

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.



Theoretical Numerical Analysis

Author : Kendall Atkinson

Publisher : Springer Science & Business Media

Page : 472 pages

File Size : 20,89 MB

Release : 2001-03-09

Category : Mathematics

ISBN : 0387951423

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Book Description

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.



Fundamentals of Engineering Numerical Analysis

Author : Parviz Moin

Publisher : Cambridge University Press

Page : 257 pages

File Size : 11,39 MB

Release : 2010-08-23

Category : Technology & Engineering

ISBN : 1139489550

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Book Description

Since the original publication of this book, available computer power has increased greatly. Today, scientific computing is playing an ever more prominent role as a tool in scientific discovery and engineering analysis. In this second edition, the key addition is an introduction to the finite element method. This is a widely used technique for solving partial differential equations (PDEs) in complex domains. This text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs for all the worked examples are now available at www.cambridge.org/Moin, and more than 30 exercises have been added. This thorough and practical book is intended as a first course in numerical analysis, primarily for new graduate students in engineering and physical science. Along with mastering the fundamentals of numerical methods, students will learn to write their own computer programs using standard numerical methods.