Computational Physics - Cristian C. Bordeianu

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Résumé :

The classic in the field for more than 25 years, now with increased emphasis on data science and new chapters on quantum computing, machine learning (AI), and general relativity

Computational physics combines physics, applied mathematics, and computer science in a cutting-edge multidisciplinary approach to solving realistic physical problems. It has become integral to modern physics research because of its capacity to bridge the gap between mathematical theory and real-world system behavior.

Computational Physics provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. Its philosophy is rooted in learning by doing, assisted by many sample programs in the popular Python programming language. The first third of the book lays the fundamentals of scientific computing, including programming basics, stable algorithms for differentiation and integration, and matrix computing. The latter two-thirds of the textbook cover more advanced topics such linear and nonlinear differential equations, chaos and fractals, Fourier analysis, nonlinear dynamics, and finite difference and finite elements methods. A particular focus in on the applications of these methods for solving realistic physical problems.

Readers of the fourth edition of Computational Physics will also find:

• An exceptionally broad range of topics, from simple matrix manipulations to intricate computations in nonlinear dynamics
• A whole suite of supplementary material: Python programs, Jupyter notebooks and videos

Computational Physics is ideal for students in physics, engineering, materials science, and any subjects drawing on applied physics....

Biographie:

Preface xvii

Acknowledgments xix

Part I Basics 1

1 Introduction 3

1.1 Computational Physics and Science 3

1.2 This Book's Subjects 4

1.3 Video Lecture Supplements 4

1.4 This Book's Codes and Problems 5

1.5 Our Language: The Python Ecosystem 6

1.6 The Easy Way: Python Distributions 6

2 Software Basics 9

2.1 Making Computers Obey 9

2.2 Computer Number Representations 11

2.3 Python Mini Tutorial 18

2.4 Programming Warmup 25

2.5 Python's Visualization Tools 30

2.6 Plotting Exercises 36

2.7 Code Listings 38

3 Errors and Uncertainties 44

3.1 Types of Errors 44

3.2 Experimental Error Investigation 49

3.3 Errors with Power Series 52

3.4 Errors in Bessel Functions 55

3.5 Code Listing 58

4 Monte Carlo Simulations 59

4.1 Random Numbers 59

4.2 Simulating a Random Walk 63

4.3 Spontaneous Decay 68

4.4 Testing and Generating Random Distributions 71

4.5 Code Listings 73

5 Differentiation and Integration 78

5.1 Differentiation Algorithms 78

5.2 Extrapolated Difference 80

5.3 Integration Algorithms 83

5.4 Gaussian Quadrature 89

5.5 Monte Carlo Integrations 91

5.6 Mean Value and N-D Integration 94

5.7 mc Variance Reduction 96

5.8 Importance Sampling and von Neumann Rejection 96

5.9 Code Listings 97

6 Trial-and-Error Searching and Data Fitting 100

6.1 Quantum Bound States I 100

6.2 Bisection Search 101

6.3 Newton-Raphson Search 102

6.4 Magnetization Search 105

6.5 Data Fitting 107

6.6 Fitting Exponential Decay 112

6.7 Least-Squares Fitting 113

6.8 Nonlinear Fit to a Resonance 118

6.9 Code Listings 120

7 Matrix Computing and N-D Searching 123

7.1 Masses on a String and N-D Searching 123

7.2 Matrix Generalities 126

7.3 Matrices in Python 129

7.4 Exercise: Tests Before Use 136

7.5 Solution to String Problem 139

7.6 Spin States and Hyperfine Structure 139

7.7 Speeding Up Matrix Computing ? 141

7.8 Code Listing 144

8 Differential Equations and Nonlinear Oscillations 147

8.1 Nonlinear Oscillators 147

8.2 ODE Review 149

8.3 Dynamic Form of ODEs 150

8.4 ODE Algorithms 152

8.5 Solution for Nonlinear Oscillations 157

8.6 Extensions: Nonlinear Resonances, Beats, Friction 159

8.7 Code Listings 161

Part II Data Science 165

9 Fourier Analyses 167

9.1 Fourier Series 167

9.2 Fourier Transforms 170

9.3 Discrete Fourier Transforms 172

9.4 Noise Filtering 178

9.5 Fast Fourier Transform ? 185

9.6 FFT Implementation 189

9.7 FFT Assessment 190

9.8 Code Listings 190

10 Wavelet and Principal Components Analysis 193

10.1 Part I: Wavelet Analysis 193

10.2 Wave Packets and Uncertainty Principle 195

10.3 Short-Time Fourier Transforms 197

10.4 Wavelet Transforms 198

10.5 Discrete Wavelet Transforms ? 203

10.6 Part II: Principal Components Analysis 213

10.7 Code Listings 220

11 Neural Networks and Machine Learning 224

11.1 Part I: Biological and Artificial Neural Networks 225

11.2 A Simple Neural Network 226

11.3 A Graphical Deep Net 232

11.4 Part II: Machine Learning Software 234

11.5 TensorFlow and SkLearn Examples 235

11.6 ml Clustering 240

11.7 Keras: Python's Deep Learning API 244

11.8 Image Processing with OpenCV 244

11.9 Explore ML Dat...

Sommaire:

Rubin H. Landau, PhD, is Professor Emeritus in the Department of Physics at Oregon State University, Corvallis, Oregon, USA. In his long and distinguished research career he has been instrumental in the development of computational physics as a defined subject, and founded both the Computational Physics Degree Program and the Northwest Alliance for Computational Science and Engineering.

Manuel J. P?ez, PhD, is a Professor in the Department of Physics at the University of Antioquia in Medellin, Colombia. He teaches courses in both physics and programming, and he and Professor Landau have collaborated on pathbreaking computational physics investigations.

Cristian C. Bordeianu, PhD, taught Physics and Computer Science at the Military College Stefan cel Mare, Campulung Moldovenesc, Romania....