| Edition |
First edition. |
| Description |
1 online resource (xvii, 638 pages) : illustrations (some colour) |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 629-633) and index. |
| Contents |
Machine generated contents note: 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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Note continued: 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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Note continued: 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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Note continued: 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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Note continued: 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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Note continued: 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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Note continued: 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. |
| Summary |
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 methodswith data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from:· statistics, · |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
MATLAB.
|
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MATLAB. |
|
MATLAB. |
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Science -- Data processing.
|
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Science -- Data processing. |
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Numerical analysis.
|
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Numerical analysis. |
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Differential equations.
|
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Differential equations. |
| Genre/Form |
Electronic books.
|
| Added Title |
Data-driven modeling and scientific computation |
| Other Form: |
Print version: Kutz, Jose Nathan. Data-driven modeling & scientific computation. First edition 9780199660339 (DLC) 2013937977 (OCoLC)858608087 |
| ISBN |
9780191635878 (electronic book) |
|
0191635871 (electronic book) |
|
1299807135 |
|
9781299807136 |
|
9780199660339 |
|
0199660336 |
|
9780199660346 |
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0199660344 |
|
