Introduction to Scientific Computing and Data Analysis

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Springer, May 30, 2016 - Computers - 497 pages
This textbook provides and 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 MATLAB codes used to produce most of the figures and data tables in the text are available on the author’s website and SpringerLink.

 

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Contents

1 Introduction to Scientific Computing
1
2 Solving A Nonlinear Equation
31
3 Matrix Equations
71
4 Eigenvalue Problems
121
5 Interpolation
182
6 Numerical Integration
231
7 Initial Value Problems
275
8 Optimization
326
9 Data Analysis
397
A Taylors Theorem
453
B BSplines
459
C Summary Tables
462
References
469
Index
483
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About the author (2016)

Mark Holmes is a Professor at Rensselaer Polytechnic Institute. His current research interests include mechanoreception and sleep-wake cycles. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.

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