# Numerical Methods

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## An Introduction to Numerical Methods and Analysis

Author : James F. Epperson
Publisher : John Wiley & Sons
Release : 2013-06-06
ISBN : 1118626230
Language : En, Es, Fr & De

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.

## Introduction to Numerical Analysis

Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475722729
Language : En, Es, Fr & De

Book Description :

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

## Stochastic Numerical Methods

Author : Raúl Toral,Pere Colet
Publisher : John Wiley & Sons
Release : 2014-06-26
ISBN : 3527683127
Language : En, Es, Fr & De

Book Description :

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations

## Elementary Differential Equations

Author : William Trench
Publisher : Brooks/Cole Publishing Company
Release : 2000-03-28
ISBN : 9780534360849
Language : En, Es, Fr & De

Book Description :

Homework help! Worked-out solutions to select problems in the text.

## A Graduate Introduction to Numerical Methods

Author : Robert M. Corless,Nicolas Fillion
Publisher : Springer Science & Business Media
Release : 2013-12-12
ISBN : 1461484537
Language : En, Es, Fr & De

Book Description :

This book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well some Matlab codes provided online as supplementary material. “I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine A Graduate Introduction to Numerical Methods and Backward Error Analysis” has been selected by Computing Reviews as a notable book in computing in 2013. Computing Reviews Best of 2013 list consists of book and article nominations from reviewers, CR category editors, the editors-in-chief of journals, and others in the computing community.

## Mathematical Modelling and Numerical Methods in Finance

Author : Anonim
Publisher : Elsevier
Release : 2009-06-16
ISBN : 0080931006
Language : En, Es, Fr & De

Book Description :

Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field

## Numerical Methods in Economics

Author : Kenneth L. Judd
Publisher : MIT Press
Release : 1998-09-28
ISBN : 9780262100717
Language : En, Es, Fr & De

Book Description :

To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.

## Numerical Methods

Author : Germund Dahlquist,Åke Björck
Publisher : Courier Corporation
Release : 2012-04-26
ISBN : 0486139468
Language : En, Es, Fr & De

Book Description :

DIVPractical text strikes balance between students' requirements for theoretical treatment and the needs of practitioners, with best methods for both large- and small-scale computing. Many worked examples and problems. 1974 edition. /div

## Computer Oriented Numerical Methods

Author : N Datta
Publisher : Vikas Publishing House
Release : 2004
ISBN : 9788125914242
Language : En, Es, Fr & De

Book Description :

This book clearly presents the algorithms required for easy implementation of numerical methods in computer programming. The book deals with the important topics of numerical methods, including errors in numerical computation, in a lucid style. Chapter-end short questions with answers and appendices with theory questions and C programs are student-friendly feature of the book.

## Numerical Methods that Work

Author : Forman S. Acton
Publisher : American Mathematical Soc.
Release : 2020-07-31
ISBN : 147045727X
Language : En, Es, Fr & De

Book Description :

Download Numerical Methods that Work book written by Forman S. Acton, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

## Efficient Numerical Methods for Non local Operators

Author : Steffen Börm
Publisher : European Mathematical Society
Release : 2010
ISBN : 9783037190913
Language : En, Es, Fr & De

Book Description :

Hierarchical matrices present an efficient way of treating dense matrices that arise in the context of integral equations, elliptic partial differential equations, and control theory. While a dense $n\times n$ matrix in standard representation requires $n^2$ units of storage, a hierarchical matrix can approximate the matrix in a compact representation requiring only $O(n k \log n)$ units of storage, where $k$ is a parameter controlling the accuracy. Hierarchical matrices have been successfully applied to approximate matrices arising in the context of boundary integral methods, to construct preconditioners for partial differential equations, to evaluate matrix functions, and to solve matrix equations used in control theory. $\mathcal{H}^2$-matrices offer a refinement of hierarchical matrices: Using a multilevel representation of submatrices, the efficiency can be significantly improved, particularly for large problems. This book gives an introduction to the basic concepts and presents a general framework that can be used to analyze the complexity and accuracy of $\mathcal{H}^2$-matrix techniques. Starting from basic ideas of numerical linear algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers in numerical mathematics and scientific computing. Special techniques are required only in isolated sections, e.g., for certain classes of model problems.

## Numerical Methods of Statistics

Author : John F. Monahan
Publisher : Cambridge University Press
Release : 2011-04-18
ISBN : 1139498002
Language : En, Es, Fr & De

Book Description :

This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.

## Numerical Methods

Author : Taylor & Francis Group,Wolfgang Boehm
Publisher : A K PETERS
Release : 2020-09-30
ISBN : 9781138413177
Language : En, Es, Fr & De

Book Description :

This book is written for engineers and other practitioners using numerical methods in their work and serves as a textbook for courses in applied mathematics and numerical analysis.

## EBOOK Applied Numerical Methods with MATLAB for Engineers and Scientists

Author : Steven Chapra
Publisher : McGraw Hill
Release : 2011-05-16
ISBN : 0077144880
Language : En, Es, Fr & De

Book Description :

Steven Chapra’s Applied Numerical Methods with MATLAB, third edition, is written for engineering and science students who need to learn numerical problem solving. Theory is introduced to inform key concepts which are framed in applications and demonstrated using MATLAB. The book is designed for a one-semester or one-quarter course in numerical methods typically taken by undergraduates. The third edition features new chapters on Eigenvalues and Fourier Analysis and is accompanied by an extensive set of m-files and instructor materials.

## Numerical Methods for Evolutionary Differential Equations

Author : Uri M. Ascher
Publisher : SIAM
Release : 2008-09-04
ISBN : 0898716527
Language : En, Es, Fr & De

Book Description :

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.

## Numerical Methods for Diffusion Phenomena in Building Physics

Author : Nathan Mendes,Marx Chhay,Julien Berger,Denys Dutykh
Publisher : Springer Nature
Release : 2019-11-29
ISBN : 3030315746
Language : En, Es, Fr & De

Book Description :

This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.

## Introduction to Numerical Methods for Water Resources

Author : W. L. Wood
Publisher : Oxford University Press
Release : 1993
ISBN : 9780198596905
Language : En, Es, Fr & De

Book Description :

Numerical methods provide a powerful and essential tool for the solution of problems of water resources. This book gives an elementary introduction to the methods in current use. Their application to surface and subsurface flow and to water quality modelling are described in this useful volume, which contains many helpful references to the literature.

## Numerical Methods in Finance

Author : Michèle Breton,Hatem Ben-Ameur
Publisher : Springer Science & Business Media
Release : 2005-12-05
ISBN : 0387251189
Language : En, Es, Fr & De

Book Description :

GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the U- versite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the devel- ment of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools.

## Numerical Methods for Least Squares Problems

Author : Ake Bjorck
Publisher : SIAM
Release : 1996-01-01
ISBN : 9781611971484
Language : En, Es, Fr & De

Book Description :

The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.