Fundamentals of Scientific Computing PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fundamentals of Scientific Computing PDF full book. Access full book title Fundamentals of Scientific Computing by Bertil Gustafsson. Download full books in PDF and EPUB format.
Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3642194958
Category : Mathematics
Languages : en
Pages : 326
Get Book
Book Description
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.
Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3642194958
Category : Mathematics
Languages : en
Pages : 326
Get Book
Book Description
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.
Author: Einar Smith
Publisher: Springer Nature
ISBN: 3030608085
Category : Mathematics
Languages : en
Pages : 344
Get Book
Book Description
The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing. The fact that different languages are studied and compared also makes the book useful for mathematicians and practitioners trying to decide which programming language to use for which purposes.
Author: Tobin A. Driscoll
Publisher: SIAM
ISBN: 1611975085
Category : Science
Languages : en
Pages : 583
Get Book
Book Description
Fundamentals of Numerical Computation?is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking. The authors have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book. The book is intended for advanced undergraduates in math, applied math, engineering, or science disciplines, as well as for researchers and professionals looking for an introduction to a subject they missed or overlooked in their education.?
Author: Michael T. Heath
Publisher: SIAM
ISBN: 1611975573
Category : Science
Languages : en
Pages : 567
Get Book
Book Description
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
Author: Timo Heister
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110988453
Category : Computers
Languages : en
Pages : 184
Get Book
Book Description
Scientific Computing for Scientists and Engineers is designed to teach undergraduate students relevant numerical methods and required fundamentals in scientific computing. Most problems in science and engineering require the solution of mathematical problems, most of which can only be done on a computer. Accurately approximating those problems requires solving differential equations and linear systems with millions of unknowns, and smart algorithms can be used on computers to reduce calculation times from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? Scientific Computing for Scientists and Engineers covers: An introduction to a wide range of numerical methods for linear systems, eigenvalue problems, differential equations, numerical integration, and nonlinear problems; Scientific computing fundamentals like floating point representation of numbers and convergence; Analysis of accuracy and efficiency; Simple programming examples in MATLAB to illustrate the algorithms and to solve real life problems; Exercises to reinforce all topics.
Author: Victor Eijkhout
Publisher: Lulu.com
ISBN: 1257992546
Category : Algebras, Linear
Languages : en
Pages : 536
Get Book
Book Description
This is a textbook that teaches the bridging topics between numerical analysis, parallel computing, code performance, large scale applications.
Author: Mark H. Holmes
Publisher: Springer Nature
ISBN: 3031224302
Category : Computers
Languages : en
Pages : 563
Get Book
Book Description
This textbook provides an introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression-based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The codes used for most of the computational examples in the text are available on GitHub. This new edition includes material necessary for an upper division course in computational linear algebra.
Author: Joakim Sundnes
Publisher:
ISBN: 3030503569
Category : Computer programming
Languages : en
Pages : 157
Get Book
Book Description
This open access book offers an initial introduction to programming for scientific and computational applications using the Python programming language. The presentation style is compact and example-based, making it suitable for students and researchers with little or no prior experience in programming. The book uses relevant examples from mathematics and the natural sciences to present programming as a practical toolbox that can quickly enable readers to write their own programs for data processing and mathematical modeling. These tools include file reading, plotting, simple text analysis, and using NumPy for numerical computations, which are fundamental building blocks of all programs in data science and computational science. At the same time, readers are introduced to the fundamental concepts of programming, including variables, functions, loops, classes, and object-oriented programming. Accordingly, the book provides a sound basis for further computer science and programming studies.
Author: L. Ridgway Scott
Publisher: Princeton University Press
ISBN: 0691227659
Category : Computers
Languages : en
Pages : 392
Get Book
Book Description
What does Google's management of billions of Web pages have in common with analysis of a genome with billions of nucleotides? Both apply methods that coordinate many processors to accomplish a single task. From mining genomes to the World Wide Web, from modeling financial markets to global weather patterns, parallel computing enables computations that would otherwise be impractical if not impossible with sequential approaches alone. Its fundamental role as an enabler of simulations and data analysis continues an advance in a wide range of application areas. Scientific Parallel Computing is the first textbook to integrate all the fundamentals of parallel computing in a single volume while also providing a basis for a deeper understanding of the subject. Designed for graduate and advanced undergraduate courses in the sciences and in engineering, computer science, and mathematics, it focuses on the three key areas of algorithms, architecture, languages, and their crucial synthesis in performance. The book's computational examples, whose math prerequisites are not beyond the level of advanced calculus, derive from a breadth of topics in scientific and engineering simulation and data analysis. The programming exercises presented early in the book are designed to bring students up to speed quickly, while the book later develops projects challenging enough to guide students toward research questions in the field. The new paradigm of cluster computing is fully addressed. A supporting web site provides access to all the codes and software mentioned in the book, and offers topical information on popular parallel computing systems. Integrates all the fundamentals of parallel computing essential for today's high-performance requirements Ideal for graduate and advanced undergraduate students in the sciences and in engineering, computer science, and mathematics Extensive programming and theoretical exercises enable students to write parallel codes quickly More challenging projects later in the book introduce research questions New paradigm of cluster computing fully addressed Supporting web site provides access to all the codes and software mentioned in the book
Author: Germund Dahlquist
Publisher: SIAM
ISBN: 0898716446
Category : Mathematics
Languages : en
Pages : 741
Get Book
Book Description
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.
