Principles Of Numerical Analysis
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Author | : Alston S. Householder |
Publisher | : Courier Corporation |
Total Pages | : 292 |
Release | : 2006-01-01 |
Genre | : Mathematics |
ISBN | : 048645312X |
Computer science rests upon the building blocks of numerical analysis. This concise treatment by an expert covers the essentials of the solution of finite systems of linear and nonlinear equations as well as the approximate representation of functions. A final section provides 54 problems, subdivided according to chapter. 1953 edition.
Author | : Ferenc Szidarovszky |
Publisher | : Springer |
Total Pages | : 352 |
Release | : 1978 |
Genre | : Mathematics |
ISBN | : |
Approximation and interpolation of functions; Numerical differentiation and integration; General theory for iteration methods; Solution of nonlinear equations; The solution of simultaneous linear equations; The solution of matrix eigenvalue problems; The numerical solution of ordinary differential equations; The numerical solution of partial differential equations.
Author | : Larkin Ridgway Scott |
Publisher | : Princeton University Press |
Total Pages | : 342 |
Release | : 2011-04-18 |
Genre | : Mathematics |
ISBN | : 1400838967 |
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 | : Stanley Dunn |
Publisher | : Elsevier |
Total Pages | : 628 |
Release | : 2005-11-21 |
Genre | : Science |
ISBN | : 0080470807 |
Numerical Modeling in Biomedical Engineering brings together the integrative set of computational problem solving tools important to biomedical engineers. Through the use of comprehensive homework exercises, relevant examples and extensive case studies, this book integrates principles and techniques of numerical analysis. Covering biomechanical phenomena and physiologic, cell and molecular systems, this is an essential tool for students and all those studying biomedical transport, biomedical thermodynamics & kinetics and biomechanics. - Supported by Whitaker Foundation Teaching Materials Program; ABET-oriented pedagogical layout - Extensive hands-on homework exercises
Author | : Victor S. Ryaben'kii |
Publisher | : CRC Press |
Total Pages | : 564 |
Release | : 2006-11-02 |
Genre | : Mathematics |
ISBN | : 1000738280 |
A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An access
Author | : Srimanta Pal |
Publisher | : Oxford Higher Education |
Total Pages | : 812 |
Release | : 2009 |
Genre | : Technology & Engineering |
ISBN | : 9780195693751 |
With an objective to provide a firm understanding of the basic concepts of numerical methods, the book provides introductory chapters on number systems, binary arithmetic, and programming tools and techniques for different programming languages such as C, C++, BASIC and FORTRAN. Subsequently, the book offers an exhaustive coverage of topics such as numerical solutions of linear and non-linear equations, eigenvlues and eigenvectors, linear least squares problem with interpolation and extrapolation, numerical differentiation and integration, ordinary differential equations, partial differential equations, and parabolic and elliptic partial differential equations. Written in a lucid style, the book contains a large number of solved examples and numerous end-chapter exercises to make for a student-friendly book. The book will also be useful to postgraduate students as well as to practicing numerical analysts, statisticians, and engineers.
Author | : Rainer Kress |
Publisher | : Springer Science & Business Media |
Total Pages | : 340 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461205999 |
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.
Author | : Jan S. Hesthaven |
Publisher | : SIAM |
Total Pages | : 571 |
Release | : 2018-01-30 |
Genre | : Science |
ISBN | : 1611975107 |
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research. Numerical Methods for Conservation Laws: From Analysis to Algorithms offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development; discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws; addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially nonoscillatory schemes, discontinuous Galerkin methods, and spectral methods; explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods; includes MATLAB software with which all main methods and computational results in the book can be reproduced; and demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons. Code and other supplemental material will be available online at publication.
Author | : A. C. Faul |
Publisher | : CRC Press |
Total Pages | : 304 |
Release | : 2016-03-23 |
Genre | : Mathematics |
ISBN | : 1498712193 |
This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.
Author | : George Lindfield |
Publisher | : Academic Press |
Total Pages | : 610 |
Release | : 2018-10-10 |
Genre | : Technology & Engineering |
ISBN | : 0128123702 |
The fourth edition of Numerical Methods Using MATLAB® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors' approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics. - Features many numerical algorithms, their fundamental principles, and applications - Includes new sections introducing Simulink, Kalman Filter, Discrete Transforms and Wavelet Analysis - Contains some new problems and examples - Is user-friendly and is written in a conversational and approachable style - Contains over 60 algorithms implemented as MATLAB® functions, and over 100 MATLAB® scripts applying numerical algorithms to specific examples