Numerical Mathematics
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Numerical Mathematics
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2017-01-26
Numerical Mathematics written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.
Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.
Numerical Mathematics
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Author : Günther Hämmerlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Mathematics written by Günther Hämmerlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"In truth, it is not knowledge, but learning, not possessing, but production, not being there, but travelling there, which provides the greatest pleasure. When I have completely understood something, then I turn away and move on into the dark; indeed, so curious is the insatiable man, that when he has completed one house, rather than living in it peacefully, he starts to build another. " Letter from C. F. Gauss to W. Bolyai on Sept. 2, 1808 This textbook adds a book devoted to applied mathematics to the series "Grundwissen Mathematik. " Our goals, like those of the other books in the series, are to explain connections and common viewpoints between various mathematical areas, to emphasize the motivation for studying certain prob lem areas, and to present the historical development of our subject. Our aim in this book is to discuss some of the central problems which arise in applications of mathematics, to develop constructive methods for the numerical solution of these problems, and to study the associated questions of accuracy. In doing so, we also present some theoretical results needed for our development, especially when they involve material which is beyond the scope of the usual beginning courses in calculus and linear algebra. This book is based on lectures given over many years at the Universities of Freiburg, Munich, Berlin and Augsburg.
Concise Numerical Mathematics
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Author : Robert Plato
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Concise Numerical Mathematics written by Robert Plato and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book succinctly covers the key topics of numerical methods. While it is basically a survey of the subject, it has enough depth for the student to walk away with the ability to implement the methods by writing computer programs or by applying them to problems in physics or engineering. The author manages to cover the essentials while avoiding redundancies and using well-chosen examples and exercises.The exposition is supplemented by numerous figures. Work estimates and pseudo codes are provided for many algorithms, which can be easily converted to computer programs. Topics covered include interpolation, the fast Fourier transform, iterative methods for solving systems of linear and nonlinear equations, numerical methods for solving ODEs, numerical methods for matrix eigenvalue problems, approximation theory, and computer arithmetic. In general, the author assumes only a knowledge of calculus and linear algebra. The book is suitable as a text for a first course in numerical methods for mathematics students or students in neighboring fields, such as engineering, physics, and computer science.
Numerical Methods
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Author : Anne Greenbaum
language : en
Publisher: Princeton University Press
Release Date : 2012-04
Numerical Methods written by Anne Greenbaum and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04 with Computers categories.
Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online.
Numerical Mathematics
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Author : Shlomo Breuer
language : en
Publisher: Cambridge University Press
Release Date : 1993-07-30
Numerical Mathematics written by Shlomo Breuer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-30 with Mathematics categories.
Numerical Mathematics is a unique book that introduces computational microcomputer laboratories as a vehicle for teaching algorithmic aspects of mathematics. This is achieved through a sequence of laboratory assignments, presupposing no previous knowledge of calculus or linear algebra, where the "chalk- and-talk" lecturer turns into a laboratory istructor. The computational assignments cover iterative processes, area approximations, linear systems, convergence acceleration, interpolative approximations, and construction of computer-library functions. The material is part and parcel of the mathematical foundations that should be acquired by a college student in the microcomputer era.
Numerical Mathematics
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Author : Matheus Grasselli
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2008
Numerical Mathematics written by Matheus Grasselli and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
Numerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas. Students using Numerical Mathematics as a supplementary reference for basic mathematical courses will be encouraged to deveolp their mathematical intuition with an effective component of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject.
Numerical Mathematics
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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-30
Numerical Mathematics written by Alfio Quarteroni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-30 with Mathematics categories.
This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been
Numerical Methods In Economics
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Author : Kenneth L. Judd
language : en
Publisher: MIT Press
Release Date : 1998-09-28
Numerical Methods In Economics written by Kenneth L. Judd and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-28 with Business & Economics categories.
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 Mathematics
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Author : Jeffrey S. Ovall
language : en
Publisher: SIAM
Release Date : 2024-10-24
Numerical Mathematics written by Jeffrey S. Ovall and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-24 with Mathematics categories.
This textbook introduces key numerical algorithms used for problems arising in three core areas of scientific computing: calculus, differential equations, and linear algebra. Theoretical results supporting the derivation and error analysis of algorithms are given rigorous justification in the text and exercises, and a wide variety of detailed computational examples further enhance the understanding of key concepts. Numerical Mathematics includes topics not typically discussed in similar texts at this level, such as a Fourier-based analysis of the trapezoid rule, finite volume methods for the 2D Poisson problem, the Nyström method for approximating the solution of integral equations, and the relatively new FEAST method for targeting clusters of eigenvalues and their eigenvectors. An early emphasis is given to recognizing or deducing orders of convergence in practice, which is essential for assessing algorithm performance and debugging computational software. Numerical experiments complement many of the theorems concerning convergence, illustrating typical behavior of the associated algorithms when the assumptions of the theorems are satisfied and when they are not. This book is intended for advanced undergraduate and beginning graduate students in mathematics seeking a solid foundation in the theory and practice of scientific computing. Students and researchers in other disciplines who want a fuller understanding of the principles underlying these algorithms will also find it useful. The text is divided into three parts, corresponding to numerical methods for problems in calculus, differential equations, and linear algebra. Each part can be used for a one-term course (quarter or semester), making the book suitable for a two- or three-term sequence in numerical analysis or for largely independent courses on any of the three main topics.
Numerical Methods For Two Point Boundary Value Problems
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Author : Herbert Bishop Keller
language : en
Publisher:
Release Date : 1992
Numerical Methods For Two Point Boundary Value Problems written by Herbert Bishop Keller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
A brief, elementary yet rigorous account of practical numerical methods for solving very general two-point boundary-value problems. Advanced undergraduate level. Over 100 problems.