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Numerical Analysis

Author : Larkin Ridgway Scott

Publisher : Princeton University Press

Page : 342 pages

File Size : 30,80 MB

Release : 2011-04-18

Category : Mathematics

ISBN : 1400838967

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Book Description

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin



Computational Methods for Numerical Analysis with R

Author : James P Howard, II

Publisher : CRC Press

Page : 257 pages

File Size : 47,59 MB

Release : 2017-07-12

Category : Mathematics

ISBN : 1498723640

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Book Description

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.



Numerical Methods for Two-Point Boundary-Value Problems

Author : Herbert B. Keller

Publisher : Courier Dover Publications

Page : 417 pages

File Size : 39,90 MB

Release : 2018-11-14

Category : Mathematics

ISBN : 0486828344

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Book Description

Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.



Elementary Numerical Analysis (3Rd Ed.)

Author : Atkinson

Publisher : John Wiley & Sons

Page : 580 pages

File Size : 45,60 MB

Release : 2009-07

Category :

ISBN : 9788126508020

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Book Description

Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems.The text introduces core areas of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic.· Taylor Polynomials · Error and Computer Arithmetic · Rootfinding · Interpolation and Approximation · Numerical Integration and Differentiation · Solution of Systems of Linear Equations · Numerical Linear Algebra: Advanced Topics · Ordinary Differential Equations · Finite Difference Method for PDEs



Afternotes on Numerical Analysis

Author : G. W. Stewart

Publisher : SIAM

Page : 183 pages

File Size : 19,87 MB

Release : 1996-01-01

Category : Mathematics

ISBN : 9781611971491

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Book Description

This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner. Written by a leading expert in numerical analysis, this book is certain to be the one you need to guide you through your favorite textbook.



Elements of Numerical Analysis

Author : Radhey S. Gupta

Publisher : Cambridge University Press

Page : 778 pages

File Size : 19,36 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.



Numerical Analysis

Author : Timothy Sauer

Publisher :

Page : 608 pages

File Size : 22,53 MB

Release : 2013-07-26

Category : Numerical analysis

ISBN : 9781292023588

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Book Description

Numerical Analysis, Second Edition, is a modern and readable text for the undergraduate audience. This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers-topics such as compression, forward and backward error analysis, and iterative methods of solving equations-all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB(r) is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.



Numerical Analysis for Statisticians

Author : Kenneth Lange

Publisher : Springer Science & Business Media

Page : 606 pages

File Size : 19,60 MB

Release : 2010-05-17

Category : Business & Economics

ISBN : 1441959459

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Book Description

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.



Numerical Analysis

Author : Rainer Kress

Publisher : Springer Science & Business Media

Page : 340 pages

File Size : 35,70 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461205999

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Book Description

An introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover everything, the goal is to guide readers towards the basic ideas and general principles by way of the main and important numerical methods. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis -- indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. The text is presented in a concise and easily understandable fashion so as to be successfully mastered in a one-year course.



A First Course in Numerical Analysis

Author : Anthony Ralston

Publisher : Courier Corporation

Page : 644 pages

File Size : 31,67 MB

Release : 2001-01-01

Category : Mathematics

ISBN : 9780486414546

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Book Description

Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.