Fundamentals of Scientific Computing

Fundamentals of Scientific Computing PDF Author: Bertil Gustafsson
Publisher: Springer Science & Business Media
ISBN: 3642194958
Category : Mathematics
Languages : en
Pages : 317

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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®.

Introduction to the Tools of Scientific Computing

Introduction to the Tools of Scientific Computing PDF Author: Einar Smith
Publisher: Springer Nature
ISBN: 3030608085
Category : Mathematics
Languages : en
Pages : 344

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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.

Fundamentals of Numerical Computation

Fundamentals of Numerical Computation PDF Author: Tobin A. Driscoll
Publisher: SIAM
ISBN: 1611975085
Category : Science
Languages : en
Pages : 583

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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.?

Scientific Computing

Scientific Computing PDF Author: John A. Trangenstein
Publisher: Springer
ISBN: 3319691058
Category : Mathematics
Languages : en
Pages : 638

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Book Description
This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

Scientific Computing

Scientific Computing PDF Author: Bertil Gustafsson
Publisher: Springer
ISBN: 3319698478
Category : Mathematics
Languages : en
Pages : 271

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Book Description
This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods’ journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing – making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

Elements of Scientific Computing

Elements of Scientific Computing PDF Author: Aslak Tveito
Publisher: Springer Science & Business Media
ISBN: 3642112994
Category : Mathematics
Languages : en
Pages : 471

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Book Description
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

Scientific Computing

Scientific Computing PDF Author: Michael T. Heath
Publisher: SIAM
ISBN: 1611975573
Category : Science
Languages : en
Pages : 587

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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.

Fundamentals of Grid Computing

Fundamentals of Grid Computing PDF Author: Frederic Magoules
Publisher: CRC Press
ISBN: 1439803684
Category : Computers
Languages : en
Pages : 323

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Book Description
The integration and convergence of state-of-the-art technologies in the grid have enabled more flexible, automatic, and complex grid services to fulfill industrial and commercial needs, from the LHC at CERN to meteorological forecasting systems. Fundamentals of Grid Computing: Theory, Algorithms and Technologies discusses how the novel technologies

Introduction to Scientific Programming with Python

Introduction to Scientific Programming with Python PDF Author: Joakim Sundnes
Publisher:
ISBN: 3030503569
Category : Computer programming
Languages : en
Pages : 157

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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.

Scientific Parallel Computing

Scientific Parallel Computing PDF Author: Larkin Ridgway Scott
Publisher: Princeton University Press
ISBN: 0691227659
Category : Computers
Languages : en
Pages : 392

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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