Data-Driven Modeling and Scientific Computation: Methods for Complex Systems and Big Data

Paperback | August 27, 2013

byJ. Nathan Kutz

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The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computationalalgorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from:* statistics,* time-frequency analysis, and * low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it,showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems.Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in theengineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

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From the Publisher

The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computationalalgorithms that help synthesize, interpret and g...

Professor Kutz is the Robert Bolles and Yasuko Endo Professor of Applied Mathematics at the University of Washington. Prof. Kutz was awarded the B.S. in physics and mathematics from the University of Washington (Seattle, WA) in 1990 and the PhD in Applied Mathematics from Northwestern University (Evanston, IL) in 1994. He joined the De...
Format:PaperbackDimensions:656 pagesPublished:August 27, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199660344

ISBN - 13:9780199660346

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Table of Contents

Part I: Basic Computations and Visualization1. MATLAB Introduction2. Linear Systems3. Curve Fitting4. Numerical Differentiation and Integration5. Basic Optimization6. VisualizationPart II: Differential and Partial Differential Equations7. Initial and Boundary Value Problems of Differential Equations8. Finite Difference Methods9. Time and Space Stepping Schemes: Method of Lines10. Spectral Methods11. Finite Element MethodsPart III: Computational Methods for Data Analysis12. Statistical Methods and Their Applications13. Time-Frequency Analysis: Fourier Transforms and Wavelets14. Image Processing and Analysis15. Linear Algebra and Singular Value Decomposition16. Independent Component Analysis17. Image Recognition18. Basics of Compressed Sensing19. Dimensionality Reduction for Partial Differential Equations20. Dynamic Mode Decomposition21. Data Assimilation Methods22. Equation Free ModelingPart IV: Scientific Applications23. Applications of Differential Equations and Boundary Value Problems24. Quantum Mechanics25. Applications of Partial Differential Equations26. Applications of Data Analysis