Computational Physics - A Practical Introduction to Computational Physics and Scientific Computing (using C++)

Foreword to the Second Edition 
Foreword to the First Edition 
1 The Computer 
 1.1 The Operating System 
  1.1.1 Filesystem 
  1.1.2 Commands 
  1.1.3 Looking for Help 
 1.2 Text Processing Tools – Filters 
 1.3 Programming with Emacs 
  1.3.1 Calling Emacs 
  1.3.2 Interacting with Emacs 
  1.3.3 Basic Editing 
  1.3.4 Cut and Paste 
  1.3.5 Windows 
  1.3.6 Files and Buffers 
  1.3.7 Modes 
  1.3.8 Emacs Help 
  1.3.9 Emacs Customization 
 1.4 The C++ Programming Language 
  1.4.1 The Foundation 
 1.5 Gnuplot 
 1.6 Shell Scripting 
2 Kinematics 
 2.1 Motion on the Plane 
  2.1.1 Plotting Data 
  2.1.2 More Examples 
 2.2 Motion in Space 
 2.3 Trapped in a Box 
  2.3.1 The One Dimensional Box 
  2.3.2 Errors 
  2.3.3 The Two Dimensional Box 
 2.4 Applications 
 2.5 Problems 
3 Logistic Map 
 3.1 Introduction 
 3.2 Fixed Points and 2n   Cycles 
 3.3 Bifurcation Diagrams 
 3.4 The Newton-Raphson Method 
 3.5 Calculation of the Bifurcation Points 
 3.6 Liapunov Exponents 
 3.7 Problems 
4 Motion of a Particle 
 4.1 Numerical Integration of Newton’s Equations 
 4.2 Prelude: Euler Methods 
 4.3 Runge–Kutta Methods 
  4.3.1 A Program for the 4th Order Runge–Kutta 
 4.4 Comparison of the Methods 
 4.5 The Forced Damped Oscillator 
 4.6 The Forced Damped Pendulum 
 4.7 Appendix: On the Euler–Verlet Method 
 4.8 Appendix: 2nd order Runge–Kutta Method 
 4.9 Problems 
5 Planar Motion 
 5.1 Runge–Kutta for Planar Motion 
 5.2 Projectile Motion 
 5.3 Planetary Motion 
 5.4 Scattering 
  5.4.1 Rutherford Scattering 
  5.4.2 More Scattering Potentials 
 5.5 More Particles 
 5.6 Problems 
6 Motion in Space 
 6.1 Adaptive Stepsize Control for RK Methods 
  6.1.1 The rksuite Suite of RK Codes 
  6.1.2 Interfacing C++ Programs with Fortran 
  6.1.3 The rksuite Driver 
 6.2 Motion of a Particle in an EM Field 
 6.3 Relativistic Motion 
 6.4 Problems 
7 Electrostatics 
 7.1 Electrostatic Field of Point Charges 
 7.2 The Program – Appetizer and ... Desert 
 7.3 The Program – Main Dish 
 7.4 The Program - Conclusion 
 7.5 Electrostatic Field in the Vacuum 
 7.6 Results 
 7.7 Poisson Equation 
 7.8 Problems 
8 Diffusion Equation 
 8.1 Introduction 
 8.2 Heat Conduction in a Thin Rod 
 8.3 Discretization 
 8.4 The Program 
 8.5 Results 
 8.6 Diffusion on the Circle 
 8.7 Analysis 
 8.8 Problems 
9 The Anharmonic Oscillator 
 9.1 Introduction 
 9.2 Calculation of the Eigenvalues of Hnm  (λ)   
 9.3 Results 
 9.4 The Double Well Potential 
 9.5 Problems 
10 Time Independent Schrödinger Equation 
 10.1 Introduction 
 10.2 The Infinite Potential Well 
 10.3 Bound States 
 10.4 Measurements 
 10.5 The Anharmonic Oscillator - Again... 
 10.6 The Lennard–Jones Potential 
 10.7 Problems 
11 The Random Walker 
 11.1 (Pseudo)Random Numbers 
 11.2 Using Pseudorandom Number Generators 
 11.3 The MIXMAX Random Number Generator 
 11.4 Random Walks 
 11.5 Problems 
12 Monte Carlo Simulations 
 12.1 Statistical Physics 
 12.2 Entropy 
 12.3 Fluctuations 
 12.4 Correlation Functions 
 12.5 Sampling 
  12.5.1 Simple Sampling 
  12.5.2 Importance Sampling 
 12.6 Markov Processes 
 12.7 Detailed Balance Condition 
 12.8 Problems 
13 Simulation of the d = 2   Ising Model 
 13.1 The Ising Model 
 13.2 Metropolis 
 13.3 Implementation 
  13.3.1 The Program 
  13.3.2 Towards a Convenient User Interface 
 13.4 Thermalization 
 13.5 Autocorrelations 
 13.6 Statistical Errors 
  13.6.1 Errors of Independent Measurements 
  13.6.2 Jackknife 
  13.6.3 Bootstrap 
 13.7 Appendix: Autocorrelation Function 
 13.8 Appendix: Error Analysis 
  13.8.1 The Jackknife Method 
  13.8.2 The Bootstrap Method 
  13.8.3 Comparing the Methods 
 13.9 Problems 
14 Critical Exponents 
 14.1 Critical Slowing Down 
 14.2 Wolff Cluster Algorithm 
 14.3 Implementation 
  14.3.1 The Program 
 14.4 Production 
 14.5 Data Analysis 
 14.6 Autocorrelation Times 
 14.7 Temperature Scaling 
 14.8 Finite Size Scaling 
 14.9 Calculation of β
 c   
 14.10 Studying Scaling with Collapse 
 14.11 Binder Cumulant 
 14.12 Appendix: Scaling 
  14.12.1 Binder Cumulant 
  14.12.2 Scaling 
  14.12.3 Finite Size Scaling 
 14.13 Appendix: Critical Exponents 
  14.13.1 Definitions 
  14.13.2 Hyperscaling Relations 
 14.14 Problems 
Bibliography 
Index