Data-Driven Modeling & Scientific Computation by Kutz, J. Nathan;

Methods for Complex Systems & Big Data

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A termék adatai:

Kiadó OUP Oxford
Megjelenés dátuma 2013. augusztus 8.

ISBN 9780199660339
Kötéstípus Keménykötés
Terjedelem658 oldal
Méret 254x195x38 mm
Súly 1524 g
Nyelv angol
Illusztrációk 200 b/w line drawings, 20 b/w halftones

Kategóriák

Analízis Alkalmazott matematika Számítógépes programozás általában Adatelemzés Mesterséges intelligencia

Rövid leírás:

Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.

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Hosszú leírás:

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 computational algorithms 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 the engineering, 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.

The book allows methods for dealing with large data to be explained in a logical process suitable for both undergraduate and post-graduate students ... With sport performance analysis evolving into deal with big data, the book forms a key bridge between mathematics and sport science

Több

Tartalomjegyzék:

I Basic Computations and Visualization
MATLAB Introduction
Linear Systems
Curve Fitting
Numerical Differentiation and Integration
Basic Optimization
Visualization
II Differential and Partial Differential Equations
Initial and Boundary Value Problems of Differential Equations144
Finite Difference Methods
Time and Space Stepping Schemes: Method of Lines
Spectral Methods
Finite Element Methods
III Computational Methods for Data Analysis
Statistical Methods and Their Applications
Time-Frequency Analysis: Fourier Transforms and Wavelets
Image Processing and Analysis
Linear Algebra and Singular Value Decomposition
Independent Component Analysis
Image Recognition
Basics of Compressed Sensing
Dimensionality Reduction for Partial Differential Equations
Dynamic Mode Decomposition
Data Assimilation Methods
Equation Free Modeling
IV Scientific Applications
Applications of Differential Equations and Boundary Value Problems
Quantum Mechanics
Applications of Partial Differential Equations
Applications of Data Analysis