Overview
Explanations of the most basic and fundamental mathematical and numerical principles that makes a thorough understanding of advanced methods easy
A unified approach demonstrating the power of mathematics when applied to different types of problems in mathematical and numerical analysis
An introductory tutorial for those who have forgotten their calculus and linear algebra, or never had much of it
Presentation of important applications in physics and engineering, representing the most significant types of mathematical models
Numerous illustrations for ease of understanding
Includes supplementary material: sn.pub/extras
Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 8)
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Table of contents (20 chapters)
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Front Matter
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Models and Elementary Mathematics
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Front Matter
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Models and elementary mathematics
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Fundamentals in Numerical Analysis
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Front Matter
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Fundamentals in numerical analysis
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Numerical Methods for Differential Equations
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Front Matter
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Numerical methods for differential equations
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Numerical Methods for Algebraic Equations
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Front Matter
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Numerical methods for algebraic equations
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Applications
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Front Matter
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Keywords
About this book
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®.
Reviews
From the reviews:
“Scientific computing is considered to comprise mathematical modeling, numerical analysis as well as issues of programming and implementation. Correspondingly, the book introduces all areas required and structures the material in 5 parts, altogether comprising 19 chapters. … In summary, the books presents the fundamentals of scientific computing in such a way that students from mathematics as well as from science or engineering can benefit.” (Gudula Rünger, Zentralblatt MATH, March, 2012)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fundamentals of Scientific Computing
Authors: Bertil Gustafsson
Series Title: Texts in Computational Science and Engineering
DOI: https://doi.org/10.1007/978-3-642-19495-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-19494-8Published: 12 June 2011
Softcover ISBN: 978-3-642-26864-9Published: 03 August 2013
eBook ISBN: 978-3-642-19495-5Published: 11 June 2011
Series ISSN: 1611-0994
Series E-ISSN: 2197-179X
Edition Number: 1
Number of Pages: XIV, 326
Topics: Computational Mathematics and Numerical Analysis, Computational Science and Engineering, Computer Appl. in Life Sciences, Mathematical and Computational Engineering, Numerical and Computational Physics, Simulation, Simulation and Modeling