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BL
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| Record Number
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624561
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dltt
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| Main Entry
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Kutz, Jose Nathan
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| Title & Author
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Data-Driven Modeling Scientific Computation : : Methods for Complex Systems Big Data /\ J. Nathan Kutz, Department of Applied Mathematics, University of Washington
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| Edition Statement
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First edition
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| Page. NO
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xvii, 638 pages :: illustrations (some color) ;; 26 cm
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| ISBN
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9780199660339 (hardback)
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: 0199660336 (hardback)
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: 9780199660346 (paperback)
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: 0199660344 (paperback)
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| Bibliographies/Indexes
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Includes bibliographical references (pages [629]-633) and index
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| Contents
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pt. I Basic Computations and Visualization -- 1.MATLAB Introduction -- 1.1.Vectors and Matrices -- 1.2.Logic, Loops and Iterations -- 1.3.Iteration: The Newton-Raphson Method -- 1.4.Function Calls, Input/Output Interactions and Debugging -- 1.5.Plotting and Importing/Exporting Data -- 2.Linear Systems -- 2.1.Direct Solution Methods for Ax = b -- 2.2.Iterative Solution Methods for Ax = b -- 2.3.Gradient (Steepest) Descent for Ax = b -- 2.4.Eigenvalues, Eigenvectors and Solvability -- 2.5.Eigenvalues and Eigenvectors for Face Recognition -- 2.6.Nonlinear Systems -- 3.Curve Fitting -- 3.1.Least-Square Fitting Methods -- 3.2.Polynomial Fits and Splines -- 3.3.Data Fitting with MATLAB -- 4.Numerical Differentiation and Integration -- 4.1.Numerical Differentiation -- 4.2.Numerical Integration -- 4.3.Implementation of Differentiation and Integration -- 5.Basic Optimization -- 5.1.Unconstrained Optimization (Derivative-Free Methods) --
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5.2.Unconstrained Optimization (Derivative Methods) -- 5.3.Linear Programming -- 5.4.Simplex Method -- 5.5.Genetic Algorithms -- 6.Visualization -- 6.1.Customizing Plots and Basic 2D Plotting -- 6.2.More 2D and 3D Plotting -- 6.3.Movies and Animations -- pt. II Differential and Partial Differential Equations -- 7.Initial and Boundary Value Problems of Differential Equations -- 7.1.Initial Value Problems: Euler, Runge-Kutta and Adams Methods -- 7.2.Error Analysis for Time-Stepping Routines -- 7.3.Advanced Time-Stepping Algorithms -- 7.4.Boundary Value Problems: The Shooting Method -- 7.5.Implementation of Shooting and Convergence Studies -- 7.6.Boundary Value Problems: Direct Solve and Relaxation -- 7.7.Implementing MATLAB for Boundary Value Problems -- 7.8.Linear Operators and Computing Spectra -- 8.Finite Difference Methods -- 8.1.Finite Difference Discretization -- 8.2.Advanced Iterative Solution Methods for Ax = b --
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8.3.Fast Poisson Solvers: The Fourier Transform -- 8.4.Comparison of Solution Techniques for Ax = b: Rules of Thumb -- 8.5.Overcoming Computational Difficulties -- 9.Time and Space Stepping Schemes: Method of Lines -- 9.1.Basic Time-Stepping Schemes -- 9.2.Time-Stepping Schemes: Explicit and Implicit Methods -- 9.3.Stability Analysis -- 9.4.Comparison of Time-Stepping Schemes -- 9.5.Operator Splitting Techniques -- 9.6.Optimizing Computational Performance: Rules of Thumb -- 10.Spectral Methods -- 10.1.Fast Fourier Transforms and Cosine/Sine Transform -- 10.2.Chebychev Polynomials and Transform -- 10.3.Spectral Method Implementation -- 10.4.Pseudo-Spectral Techniques with Filtering -- 10.5.Boundary Conditions and the Chebychev Transform -- 10.6.Implementing the Chebychev Transform -- 10.7.Computing Spectra: The Floquet-Fourier-Hill Method -- 11.Finite Element Methods -- 11.1.Finite Element Basis -- 11.2.Discretizing with Finite Elements and Boundaries --
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11.3.MATLAB for Partial Differential Equations -- 11.4.MATLAB Partial Differential Equations Toolbox -- pt. III Computational Methods for Data Analysis -- 12.Statistical Methods and Their Applications -- 12.1.Basic Probability Concepts -- 12.2.Random Variables and Statistical Concepts -- 12.3.Hypothesis Testing and Statistical Significance -- 13.Time-Frequency Analysis: Fourier Transforms and Wavelets -- 13.1.Basics of Fourier Series and the Fourier Transform -- 13.2.FFT Application: Radar Detection and Filtering -- 13.3.FFT Application: Radar Detection and Averaging -- 13.4.Time-Frequency Analysis: Windowed Fourier Transforms -- 13.5.Time-Frequency Analysis and Wavelets -- 13.6.Multi-Resolution Analysis and the Wavelet Basis -- 13.7.Spectrograms and the Gabor Transform in MATLAB -- 13.8.MATLAB Filter Design and Wavelet Toolboxes -- 14.Image Processing and Analysis -- 14.1.Basic Concepts and Analysis of Images --
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14.2.Linear Filtering for Image Denoising -- 14.3.Diffusion and Image Processing -- 15.Linear Algebra and Singular Value Decomposition -- 15.1.Basics of the Singular Value Decomposition (SVD) -- 15.2.The SVD in Broader Context -- 15.3.Introduction to Principal Component Analysis (PCA) -- 15.4.Principal Components, Diagonalization and SVD -- 15.5.Principal Components and Proper Orthogonal Modes -- 15.6.Robust PCA -- 16.Independent Component Analysis -- 16.1.The Concept of Independent Components -- 16.2.Image Separation Problem -- 16.3.Image Separation and MATLAB -- 17.Image Recognition: Basics of Machine Learning -- 17.1.Recognizing Dogs and Cats -- 17.2.The SVD and Linear Discrimination Analysis -- 17.3.Implementing Cat/Dog Recognition in MATLAB -- 18.Basics of Compressed Sensing -- 18.1.Beyond Least-Square Fitting: The L1 Norm -- 18.2.Signal Reconstruction and Circumventing Nyquist -- 18.3.Data (Image) Reconstruction from Sparse Sampling --
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19.Dimensionality Reduction for Partial Differential Equations -- 19.1.Modal Expansion Techniques for PDEs -- 19.2.PDE Dynamics in the Right (Best) Basis -- 19.3.Global Normal Forms of Bifurcation Structures in PDEs -- 19.4.The POD Method and Symmetries/Invariances -- 19.5.POD Using Robust PCA -- 20.Dynamic Mode Decomposition -- 20.1.Theory of Dynamic Mode Decomposition (DMD) -- 20.2.Dynamics of DMD Versus POD -- 20.3.Applications of DMD -- 21.Data Assimilation Methods -- 21.1.Theory of Data Assimilation -- 21.2.Data Assimilation, Sampling and Kalman Filtering -- 21.3.Data Assimilation for the Lorenz Equation -- 22.Equation-Free Modeling -- 22.1.Multi-Scale Physics: An Equation-Free Approach -- 22.2.Lifting and Restricting in Equation-Free Computing -- 22.3.Equation-Free Space-Time Dynamics -- 23.Complex Dynamical Systems: Combining Dimensionality Reduction, Compressive Sensing and Machine Learning -- 23.1.Combining Data Methods for Complex Systems --
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23.2.Implementing a Dynamical Systems Library -- 23.3.Flow Around a Cylinder: A Prototypical Example -- pt. IV Scientific Applications -- 24.Applications of Differential Equations and Boundary Value Problems -- 24.1.Neuroscience and the Hodgkin-Huxley Model -- 24.2.Celestial Mechanics and the Three-Body Problem -- 24.3.Atmospheric Motion and the Lorenz Equations -- 24.4.Quantum Mechanics -- 24.5.Electromagnetic Waveguides -- 25.Applications of Partial Differential Equations -- 25.1.The Wave Equation -- 25.2.Mode-Locked Lasers -- 25.3.Bose-Elnstein Condensates -- 25.4.Advection-Diffusion and Atmospheric Dynamics -- 25.5.Introduction to Reaction-Diffusion Systems -- 25.6.Steady State Flow Over an Airfoil -- 26.Applications of Data Analysis -- 26.1.Analyzing Music Scores and the Gabor Transform -- 26.2.Image Denoising through Filtering and Diffusion -- 26.3.Oscillating Mass and Dimensionality Reduction -- 26.4.Music Genre Identification
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| Subject
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Science-- Data processing
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Numerical analysis
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Differential equations
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| Subject
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MATLAB
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| Dewey Classification
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501.519535
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| LC Classification
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Q183.9.K88 2013
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| Parallel Title
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Data-Driven Modeling and Scientific Computation
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