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| Author | : Herbert B. Keller |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-11-14 |
| Genre | : Mathematics |
| ISBN | : 0486828344 |
Download Numerical Methods for Two-Point Boundary-Value Problems Book in PDF, ePub and Kindle
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.
| Author | : J. Stoer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 674 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475722729 |
Download Introduction to Numerical Analysis Book in PDF, ePub and Kindle
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.
| Author | : Larkin Ridgway Scott |
| Publisher | : Princeton University Press |
| Total Pages | : 342 |
| Release | : 2011-04-18 |
| Genre | : Mathematics |
| ISBN | : 1400838967 |
Download Numerical Analysis Book in PDF, ePub and Kindle
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
| Author | : Kendall Atkinson |
| Publisher | : John Wiley & Sons |
| Total Pages | : 726 |
| Release | : 1991-01-16 |
| Genre | : Mathematics |
| ISBN | : 0471624896 |
Download An Introduction to Numerical Analysis Book in PDF, ePub and Kindle
This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.
| Author | : Anthony Ralston |
| Publisher | : Courier Corporation |
| Total Pages | : 644 |
| Release | : 2001-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486414546 |
Download A First Course in Numerical Analysis Book in PDF, ePub and Kindle
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.
| Author | : Kenneth Lange |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 606 |
| Release | : 2010-05-17 |
| Genre | : Business & Economics |
| ISBN | : 1441959459 |
Download Numerical Analysis for Statisticians Book in PDF, ePub and Kindle
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.
| Author | : Walter Gautschi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 611 |
| Release | : 2011-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817682597 |
Download Numerical Analysis Book in PDF, ePub and Kindle
Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
| Author | : Brian Sutton |
| Publisher | : SIAM |
| Total Pages | : 431 |
| Release | : 2019-04-18 |
| Genre | : Mathematics |
| ISBN | : 1611975700 |
Download Numerical Analysis Book in PDF, ePub and Kindle
This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.
| Author | : James F. Epperson |
| Publisher | : John Wiley & Sons |
| Total Pages | : 579 |
| Release | : 2013-06-06 |
| Genre | : Mathematics |
| ISBN | : 1118626230 |
Download An Introduction to Numerical Methods and Analysis Book in PDF, ePub and Kindle
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.
| Author | : Timo Heister |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 193 |
| Release | : 2019-03-18 |
| Genre | : Mathematics |
| ISBN | : 3110573334 |
Download Numerical Analysis Book in PDF, ePub and Kindle
Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.
