Numerical Methods: Think before You Compute
Title | Numerical Methods: Think before You Compute PDF eBook |
Author | E. J. Hinch |
Publisher | Cambridge University Press |
Pages | 243 |
Release | 2020-04-30 |
Genre | Mathematics |
ISBN | 1108479545 |
This guide to computational fluid mechanics introduces beginning graduate students to the subject's standard methods and common pitfalls.
Numerical Methods that Work
Title | Numerical Methods that Work PDF eBook |
Author | Forman S. Acton |
Publisher | American Mathematical Soc. |
Pages | 549 |
Release | 2020-07-31 |
Genre | Mathematics |
ISBN | 147045727X |
A First Course in Numerical Methods
Title | A First Course in Numerical Methods PDF eBook |
Author | Uri M. Ascher |
Publisher | SIAM |
Pages | 574 |
Release | 2011-07-14 |
Genre | Mathematics |
ISBN | 0898719976 |
Offers students a practical knowledge of modern techniques in scientific computing.
Numerical Methods in Scientific Computing:
Title | Numerical Methods in Scientific Computing: PDF eBook |
Author | Germund Dahlquist |
Publisher | SIAM |
Pages | 741 |
Release | 2008-09-04 |
Genre | Mathematics |
ISBN | 0898716446 |
This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.
Introduction to Numerical Analysis
Title | Introduction to Numerical Analysis PDF eBook |
Author | J. Stoer |
Publisher | Springer Science & Business Media |
Pages | 674 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 1475722729 |
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.
Numerical Methods
Title | Numerical Methods PDF eBook |
Author | Anne Greenbaum |
Publisher | Princeton University Press |
Pages | 471 |
Release | 2012-04-01 |
Genre | Mathematics |
ISBN | 1400842670 |
A rigorous and comprehensive introduction to numerical analysis Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects—design, analysis, or computer implementation—of numerical algorithms, depending on the background and interests of students. 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. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online
Numerical Analysis
Title | Numerical Analysis PDF eBook |
Author | Larkin Ridgway Scott |
Publisher | Princeton University Press |
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