Introduction to Scientific Computing and Data Analysis
Introduction to Scientific Computing and Data Analysis

Author: Mark H. Holmes

Publisher: Springer Nature

Published: 2023-07-11

Total Pages: 563

ISBN-13: 3031224302

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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.

Fundamentals of Scientific Computing
Fundamentals of Scientific Computing

Author: Bertil Gustafsson

Publisher: Springer Science & Business Media

Published: 2011-06-11

Total Pages: 317

ISBN-13: 3642194958

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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®.

Scientific Computing
Scientific Computing

Author: Michael T. Heath

Publisher: SIAM

Published: 2018-11-14

Total Pages: 567

ISBN-13: 1611975573

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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.

Elements of Scientific Computing
Elements of Scientific Computing

Author: Aslak Tveito

Publisher: Springer Science & Business Media

Published: 2010-09-24

Total Pages: 471

ISBN-13: 3642112994

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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.

Introduction to Scientific Computing
Introduction to Scientific Computing

Author: Charles F. Van Loan

Publisher: Pearson

Published: 2000

Total Pages: 388

ISBN-13:

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Unique in content and approach, this book covers all the topics that are usually covered in an introduction to scientific computing--but folds in graphics and matrix-vector manipulation in a way that gets readers to appreciate the "connection" between continuous mathematics and computing. "MATLAB 5" is used "throughout" to encourage experimentation, and each chapter focuses on a different important theorem--allowing readers to appreciate the rigorous side of scientific computing. In addition to standard topical coverage, each chapter includes 1) a sketch of a "hard" problem that involves ill-conditioning, high dimension, etc.; 2)at least one theorem with both a rigorous proof and a "proof by MATLAB" experiment to bolster intuition; 3)at least one recursive algorithm; and 4)at least one connection to a real-world application. The book revolves around examples that are packaged in 200+ M-files, which, collectively, communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. Power Tools of the Trade. Polynomial Interpolation. Piecewise Polynomial Interpolation. Numerical Integration. Matrix Computations. Linear Systems. The QR and Cholesky Factorizations. Nonlinear Equations and Optimization. The Initial Value Problem. For engineers and mathematicians.

Introduction to the Tools of Scientific Computing
Introduction to the Tools of Scientific Computing

Author: Einar Smith

Publisher: Springer Nature

Published: 2020-12-02

Total Pages: 344

ISBN-13: 3030608085

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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.

Scientific Computing with MATLAB and Octave
Scientific Computing with MATLAB and Octave

Author: Alfio Quarteroni

Publisher: Springer Science & Business Media

Published: 2010-05-30

Total Pages: 379

ISBN-13: 3642124305

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Preface to the First Edition This textbook is an introduction to Scienti?c Computing. We will illustrate several numerical methods for the computer solution of c- tain classes of mathematical problems that cannot be faced by paper and pencil. We will show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of di?erential equations. With this aim, in Chapter 1 we will illustrate the rules of the game thatcomputersadoptwhenstoringandoperatingwith realandcomplex numbers, vectors and matrices. In order to make our presentation concrete and appealing we will 1 adopt the programming environment MATLAB as a faithful c- panion. We will gradually discover its principal commands, statements and constructs. We will show how to execute all the algorithms that we introduce throughout the book. This will enable us to furnish an - mediate quantitative assessment of their theoretical properties such as stability, accuracy and complexity. We will solve several problems that will be raisedthrough exercises and examples, often stemming from s- ci?c applications.

A Gentle Introduction to Scientific Computing
A Gentle Introduction to Scientific Computing

Author: Dan Stanescu

Publisher: CRC Press

Published: 2022-05-01

Total Pages: 283

ISBN-13: 0429553463

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Scientific Computation has established itself as a stand-alone area of knowledge at the borderline between computer science and applied mathematics. Nonetheless, its interdisciplinary character cannot be denied: its methodologies are increasingly used in a wide variety of branches of science and engineering. A Gentle Introduction to Scientific Computing intends to serve a very broad audience of college students across a variety of disciplines. It aims to expose its readers to some of the basic tools and techniques used in computational science, with a view to helping them understand what happens "behind the scenes" when simple tools such as solving equations, plotting and interpolation are used. To make the book as practical as possible, the authors explore their subject both from a theoretical, mathematical perspective and from an implementation-driven, programming perspective. Features Middle-ground approach between theory and implementation. Suitable reading for a broad range of students in STEM disciplines. Could be used as the primary text for a first course in scientific computing. Introduces mathematics majors, without any prior computer science exposure, to numerical methods. All mathematical knowledge needed beyond Calculus (together with the most widely used Calculus notation and concepts) is introduced in the text to make it self-contained. The erratum document for A Gentle Introduction to Scientific Computing can be accessed here.

Scientific Computing - An Introduction using Maple and MATLAB
Scientific Computing - An Introduction using Maple and MATLAB

Author: Walter Gander

Publisher: Springer Science & Business

Published: 2014-04-23

Total Pages: 926

ISBN-13: 3319043250

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Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.