Computational Physics Using C - John W Fattaruso

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Résumé :

Preface ix
About the Companion Website xiii

1 Introduction 1
1.1 What Is Computational Physics? 1
1.2 Modularizing and Reusing Code 4
1.3 Introduction to Computational Efficiency 7
1.4 Exercises 13

2 Precision Limits of Numerical Computation and Algorithms 15
2.1 Computer Numerical Representation 16
2.2 Roundoff Errors 22
2.3 Loss of Precision Errors 26
2.4 Taylor's Theorem 27
2.5 Truncation Errors 27
2.6 Introduction to Numerical C Programming 32
2.7 Exercises 34

3 C Programming Details 39
3.1 Structures and Pointers 39
3.2 Modularizing Code and Encapsulating Data in C 62
3.3 Common Coding Traps 67
3.4 Exercises 74

4 Visualization of Numerical Models 77
4.1 Coding: Function Stepper Tool 78
4.2 Application: Damped Harmonic Oscillator 82
4.3 Coding: The gnuplot Plotting Tool 85
4.4 Application: The Helmholtz Coil 89
4.5 Application: The Maxwell-Boltzmann Distribution 93
4.6 Application: Rainbows 94
4.7 Application: Diffraction Patterns 98
4.8 Application: Collisions 104
4.9 Application: Quantum Wave Packets 111
4.10 Application: Quantum Scattering 117
4.11 Application: Field Vectors 122
4.12 Application: The Thomson Problem 125
4.13 Coding: Generating Animated Graphics 126
4.14 Exercises 132

5 Roots of Nonlinear Functions 137
5.1 Algorithms: Root Finding 137
5.2 Coding: The Root Solver Tool 143
5.3 Application: The Catenary 144
5.4 Application: Kirchoff's Voltage Law 146
5.5 Application: Mechanics Problems 147
5.6 Application: Kepler's Equation 148
5.7 Application: Gravitational Lagrange Points 153
5.8 Application: Planck's Radiation Law 156
5.9 Application: Radioactive Decay 157
5.10 Coding: Finding Multiple Roots with Stepping 159
5.11 Application: Quantum Energy Levels of Bound Particles 161
5.12 Application: Ideal Single-slit Diffraction 166
5.13 Exercises 167

6 Systems of Linear Equations 169
6.1 Algorithms: Gaussian Elimination 170
6.2 Algorithms: Pivoting Strategies 171
6.3 Algorithms: The Jacobi Eigenvalue Method 172
6.4 Coding: The Systems of Linear Equations Tool 173
6.5 Application: Modes of Coupled Oscillators 176
6.6 Application: The Laplace Equation 185
6.7 Application: Kirchoff's Current Law 193
6.8 Application: Determinate Structures 195
6.9 Coding: Animated Modes of Coupled Oscillators 199
6.10 Exercises 200

7 Systems of Nonlinear Equations 203
7.1 Algorithms: Multidimensional Newton-Raphson Method 204
7.2 Coding: The Systems of Nonlinear Equations Tool 205
7.3 Application: Statics Problems 206
7.4 Application: Nonlinear Circuits 208
7.5 Application: Hyperbolic Radio Navigation 210
7.6 Algorithms: Numerical Estimates of the Jacobian Partial Derivatives 212
7.7 Application: The Covalent Bond 213
7.8 Exercises 219

8 Monte Carlo Simulation 221
8.1 Algorithms: Applications of Pseudorandom Numbers 221
8.2 Algorithms: Linear Congruential Method 223
8.3 Coding: The Pseudorandom Number Generator Tool 225
8.4 Application: Monte Carlo Simulation of ? 226
8.5 Coding: The Linux /dev/random Device 227
8.6 Application: Random Walks 228
8.7 Application: Radioactive Decay Revisited 232
8.8 Application: Classical Scattering 235
8.9 Application: Corner Pocket Shots 237
8.10 Application: Olbers' Paradox 240
8.11 Application: Ideal Gas Simulation 243
8.12 Application: Integration of Gauss' Law 247
8.13 Exercises 249

9 Interpolation of Sparse Data Points 251
9.1 Algorithms: Interpolation Methods 253
9.2 Coding:...

Biographie:

John W. Fattaruso, PhD, is Adjunct Professor at Southern Methodist University, where he teaches in the Physics, Electrical Engineering, and Computer Science departments. His expertise spans computational physics, numerical analysis, and circuit design. A former Distinguished Member of the Technical Staff at Texas Instruments, he holds 32 U.S. patents and has published widely in IEEE journals and conferences.