An Introduction to Numerical Analysis

  • Filename: an-introduction-to-numerical-analysis.
  • ISBN: 0521007941
  • Release Date: 2003-08-28
  • Number of pages: 433
  • Author: Endre Süli
  • Publisher: Cambridge University Press



Introduction to numerical analysis combining rigour with practical applications. Numerous exercises plus solutions.

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 9780534392000
  • Release Date: 2004-12-10
  • Number of pages: 850
  • Author: Richard Burden
  • Publisher: Cengage Learning



This well-respected text gives an introduction to the modern approximation techniques and explains how, why, and when the techniques can be expected to work. The authors focus on building students' intuition to help them understand why the techniques presented work in general, and why, in some situations, they fail. With a wealth of examples and exercises, the text demonstrates the relevance of numerical analysis to a variety of disciplines and provides ample practice for students. The applications chosen demonstrate concisely how numerical methods can be, and often must be, applied in real-life situations. In this edition, the presentation has been fine-tuned to make the book even more useful to the instructor and more interesting to the reader. Overall, students gain a theoretical understanding of, and a firm basis for future study of, numerical analysis and scientific computing. A more applied text with a different menu of topics is the authors' highly regarded NUMERICAL METHODS, Third Edition. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Numerical Methods

  • Filename: numerical-methods.
  • ISBN: 0486428079
  • Release Date: 2003
  • Number of pages: 573
  • Author: Germund Dahlquist
  • Publisher: Courier Corporation



Practical 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.

Dynamical Systems and Numerical Analysis

  • Filename: dynamical-systems-and-numerical-analysis.
  • ISBN: 0521645638
  • Release Date: 1998-11-28
  • Number of pages: 685
  • Author: Andrew Stuart
  • Publisher: Cambridge University Press



This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 9780817682590
  • Release Date: 2011-12-07
  • Number of pages: 588
  • Author: Walter Gautschi
  • Publisher: Springer Science & Business Media



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.

A First Course in the Numerical Analysis of Differential Equations

  • Filename: a-first-course-in-the-numerical-analysis-of-differential-equations.
  • ISBN: 0521556554
  • Release Date: 1996-01-18
  • Number of pages: 378
  • Author: Arieh Iserles
  • Publisher: Cambridge University Press



Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations.

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 9781305465350
  • Release Date: 2015-01-01
  • Number of pages: 912
  • Author: Richard L. Burden
  • Publisher: Cengage Learning



This well-respected text introduces the theory and application of modern numerical approximation techniques to students taking a one- or two-semester course in numerical analysis. Providing an accessible treatment that only requires a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind when crafted more than 30 years ago to serve a diverse undergraduate audience, Burden, Faires, and Burden's NUMERICAL ANALYSIS remains the definitive introduction to a vital and practical subject. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 1400838967
  • Release Date: 2011-04-18
  • Number of pages: 344
  • Author: L. Ridgway Scott
  • Publisher: Princeton University Press



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

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 0444506179
  • Release Date: 2001
  • Number of pages: 505
  • Author: Claude Brezinski
  • Publisher: Gulf Professional Publishing



Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

COMPUTER ORIENTED NUMERICAL METHODS

  • Filename: computer-oriented-numerical-methods.
  • ISBN: 8120307860
  • Release Date: 1993-01-01
  • Number of pages: 208
  • Author: V. RAJARAMAN
  • Publisher: PHI Learning Pvt. Ltd.



This book is a concise presentation of the basic concepts used in evolving numerical methods with special emphasis on developing computational algorithms for solving problems in algebra and calculus on a computer. It is written for undergraduate science and engineering students who have taken a first course in differential and integral calculus. The approach is to ensure conceptual understanding of the numerical methods by relying on students geometric intuition. The book provides coverage of iterative methods for solving algebraic and transcendental equations, direct and iterative methods of solving simultaneous algebraic equations, numerical methods for differen-tiation and integration, and solution of ordinary differential equations with initial conditions. The formulation of algorithms is illustrated with a number of solved examples and an algorithmic language based on English (and similar to PASCAL) is used to express the logic of the numerical procedures. This approach is thus different from that used in most books which either use a programming language like FORTRAN or use flow charts to express algorithms. The solutions to selected problems have been provided at the end of the book.

A First Course in Numerical Analysis

  • Filename: a-first-course-in-numerical-analysis.
  • ISBN: 048641454X
  • Release Date: 2001
  • Number of pages: 606
  • Author: Anthony Ralston
  • Publisher: Courier Corporation



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.

Numerical Analysis Using MATLAB and Excel

  • Filename: numerical-analysis-using-matlab-and-excel.
  • ISBN: 9781934404034
  • Release Date: 2007
  • Number of pages: 632
  • Author: Steven T. Karris
  • Publisher: Orchard Publications



This text is written primarily for students/readers who have a good background of high-school algebra, geometry, trigonometry, and the fundamentals of differential and integral calculus.

Numerical Analysis

  • Filename: numerical-analysis.
  • ISBN: 0198508522
  • Release Date: 2002
  • Number of pages: 496
  • Author: M. Schatzman
  • Publisher: Oxford University Press



Numerical analysis explains why numerical computations work - or fail. These are mathematical questions, and the book answers in kind, providing students with a very complete and sound presentation of the interface between mathematics and scientific computation. The book does not assume previous knowledge of numerical methods. It includes a large range of exercises, and will be suitable as a textbook at the advanced undergraduate level.

Numerical Methods for Ordinary Differential Equations

  • Filename: numerical-methods-for-ordinary-differential-equations.
  • ISBN: 0470753757
  • Release Date: 2008-04-15
  • Number of pages: 482
  • Author: J. C. Butcher
  • Publisher: John Wiley & Sons



In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.

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