Scientific Computation On Mathematical Problems And Conjectures
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Scientific Computation On Mathematical Problems And Conjectures
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Author : Richard S. Varga
language : en
Publisher: SIAM
Release Date : 1990-01-01
Scientific Computation On Mathematical Problems And Conjectures written by Richard S. Varga and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
This book studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures.
Scientific Computing With Mathematica
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Author : Addolorata Marasco
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scientific Computing With Mathematica written by Addolorata Marasco and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica. Topics and Features:*Explains how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving *End-of- chapter exercise sets incorporating the use of Mathematica programs *Detailed description and explanation of the mathematical procedures underlying the programs written in Mathematica *Appendix describing the use of ten notebooks to guide the reader through all the exercises. This book is an essential text/reference for students, graduates and practitioners in applied mathematics and engineering interested in ODE's problems in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-
Scientific Computation On Mathematical Problems And Conjectures
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Author : Richard S. Varga
language : en
Publisher: SIAM
Release Date : 1990-01-01
Scientific Computation On Mathematical Problems And Conjectures written by Richard S. Varga and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures. Scientific Computation on Mathematical Problems and Conjectures includes studies of the Bernstein Conjecture of 1913 in polynomial approximation theory, the "1/9" Conjecture of 1977 in rational approximation theory, the famous Riemann Hypothesis of 1859, and the Polya Conjecture of 1927. The emphasis of this monograph rests strongly on the interplay between hard analysis and high-precision calculations.
Scientific Computing With Case Studies
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Author : Dianne P. O'Leary
language : en
Publisher: SIAM
Release Date : 2009-01-01
Scientific Computing With Case Studies written by Dianne P. O'Leary and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
Open Problems In Mathematics And Computational Science
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Author : Çetin Kaya Koç
language : en
Publisher: Springer
Release Date : 2015-03-25
Open Problems In Mathematics And Computational Science written by Çetin Kaya Koç and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-25 with Computers categories.
This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.
Numerical And Symbolic Scientific Computing
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Author : Ulrich Langer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-19
Numerical And Symbolic Scientific Computing written by Ulrich Langer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-19 with Mathematics categories.
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
Mathematical Principles For Scientific Computing And Visualization
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Author : Gerald Farin
language : en
Publisher: CRC Press
Release Date : 2008-10-21
Mathematical Principles For Scientific Computing And Visualization written by Gerald Farin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-21 with Computers categories.
This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coo
Projects In Scientific Computation
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Author : Richard E. Crandall
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-06-22
Projects In Scientific Computation written by Richard E. Crandall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-22 with Computers categories.
This interdisciplinary book provides a compendium of projects, plus numerous example programs for readers to study and explore. Designed for advanced undergraduates or graduates of science, mathematics and engineering who will deal with scientific computation in their future studies and research, it also contains new and useful reference materials for researchers. The problem sets range from the tutorial to exploratory and, at times, to "the impossible". The projects were collected from research results and computational dilemmas during the authors tenure as Chief Scientist at NeXT Computer, and from his lectures at Reed College. The content assumes familiarity with such college topics as calculus, differential equations, and at least elementary programming. Each project focuses on computation, theory, graphics, or a combination of these, and is designed with an estimated level of difficulty. The support code for each takes the form of either C or Mathematica, and is included in the appendix and on the bundled diskette. The algorithms are clearly laid out within the projects, such that the book may be used with other symbolic numerical and algebraic manipulation products
Scientific Computing With Ordinary Differential Equations
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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Scientific Computing With Ordinary Differential Equations written by Peter Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area
Solving Problems In Scientific Computing Using Maple And Matlab
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Author : Walter Gander
language : en
Publisher:
Release Date : 1995-04-21
Solving Problems In Scientific Computing Using Maple And Matlab written by Walter Gander and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-21 with categories.