Навигация
Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
ОбложкаPang T. An introduction to computational physics. - 2nd ed. - Cambridge; New York: Cambridge University Press, 2006. - xv, 385 p.: ill. - Ref.: p.369-380. - Ind.: p.381-385. - ISBN 978-0-521-82569-6
Шифр: (И/В31-Р21) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
Preface to first edition ....................................... xi
Preface ...................................................... xiii
Acknowledgments ................................................ xv

1  Introduction ................................................. 1
   1.1  Computation and science ................................. 1
   1.2  The emergence of modern computers ....................... 4
   1.3  Computer algorithms and languages ....................... 7
   Exercises ................................................... 14
2  Approximation of a function ................................. 16
   2.1  Interpolation .......................................... 16
   2.2  Least-squares approximation ............................ 24
   2.3  The Millikan experiment ................................ 27
   2.4  Spline approximation ................................... 30
   2.5  Random-number generators ............................... 37
   Exercises ................................................... 44
3  Numerical calculus .......................................... 49
   3.1  Numerical differentiation .............................. 49
   3.2  Numerical integration .................................. 56
   3.3  Roots of an equation ................................... 62
   3.4  Extremes of a function ................................. 66
   3.5  Classical scattering ................................... 70
   Exercises ................................................... 76
4  Ordinary differential equations ............................. 80
   4.1  Initial-value problems ................................. 81
   4.2  The Euler and Picard methods ........................... 81
   4.3  Predictor-corrector methods ............................ 83
   4.4  The Runge-Kutta method ................................. 88
   4.5  Chaotic dynamics of a driven pendulum .................. 90
   4.6  Boundary-value and eigenvalue problems ................. 94
   4.7  The shooting method .................................... 96
   4.8  Linear equations and the Sturm-Liouville problem ....... 99
   4.9  The one-dimensional Schrödinger equation .............. 105
   Exercises .................................................. 115
5  Numerical methods for matrices ............................. 119
   5.1  Matrices in physics ................................... 119
   5.2  Basic matrix operations ............................... 123
   5.3  Linear equation systems ............................... 125
   5.4  Zeros and extremes of multivariable functions ......... 133
   5.5  Eigenvalue problems ................................... 138
   5.6  The Faddeev-Leverrier method .......................... 147
   5.7  Complex zeros of a polynomial ......................... 149
   5.8  Electronic structures of atoms ........................ 153
   5.9  The Lanczos algorithm and the many-body problem ....... 156
   5.10 Random matrices ....................................... 158
   Exercises .................................................. 160
6  Spectral analysis .......................................... 164
   6.1  Fourier analysis and orthogonal functions ............. 165
   6.2  Discrete Fourier transform ............................ 166
   6.3  Fast Fourier transform ................................ 169
   6.4  Power spectrum of a driven pendulum ................... 173
   6.5  Fourier transform in higher dimensions ................ 174
   6.6  Wavelet analysis ...................................... 175
   6.7  Discrete wavelet transform ............................ 180
   6.8  Special functions ..................................... 187
   6.9  Gaussian quadratures .................................. 191
   Exercises .................................................. 193
7  Partial differential equations ............................. 197
   7.1  Partial differential equations in physics ............. 197
   7.2  Separation of variables ............................... 198
   7.3  Discretization of the equation ........................ 204
   7.4  The matrix method for difference equations ............ 206
   7.5  The relaxation method ................................. 209
   7.6  Groundwater dynamics .................................. 213
   7.7  Initial-value problems ................................ 216
   7.8  Temperature field of a nuclear waste rod .............. 219
   Exercises .................................................. 222
8  Molecular dynamics simulations ............................. 226
   8.1   General behavior of a classical system ............... 226
   8.2  Basic methods for many-body systems ................... 228
   8.3  The Verlet algorithm .................................. 232
   8.4  Structure of atomic clusters .......................... 236
   8.5  The Gear predictor-corrector method ................... 239
   8.6  Constant pressure, temperature, and bond length ....... 241
   8.7  Structure and dynamics of real materials .............. 246
   8.8  Ab initio molecular dynamics .......................... 250
   Exercises .................................................. 254
9  Modeling continuous systems ................................ 256
   9.1  Hydrodynamic equations ................................ 256
   9.2  The basic finite element method ....................... 258
   9.3  The Ritz variational method ........................... 262
   9.4  Higher-dimensional systems ............................ 266
   9.5  The finite element method for nonlinear equations ..... 269
   9.6  The particle-in-cell method ........................... 271
   9.7  Hydrodynamics and magnetohydrodynamics ................ 276
   9.8  The lattice Boltzmann method .......................... 279
   Exercises .................................................. 282
10 Monte Carlo simulations .................................... 285
   10.1 Sampling and integration .............................. 285
   10 2 The Metropolis algorithm .............................. 287
   10.3 Applications in statistical physics ................... 292
   10.4 Critical slowing down and block algorithms ............ 297
   10.5 Variational quantum Monte Carlo simulations ........... 299
   10.6 Green's function Monte Carlo simulations .............. 303
   10.7 Two-dimensional electron gas .......................... 307
   10.8 Path-integral Monte Carlo simulations ................. 313
   10.9 Quantum lattice models ................................ 315
   Exercises .................................................. 320
11 Genetic algorithm and programming .......................... 323
   11.1 Basic elements of a genetic algorithm ................. 324
   11.2 The Thomson problem ................................... 332
   11.3 Continuous genetic algorithm .......................... 335
   11.4 Other applications .................................... 338
   11.5 Genetic programming ................................... 342
   Exercises .................................................. 345
12 Numerical renormalization .................................. 347
   12.1 The scaling concept ................................... 347
   12.2 Renormalization transform ............................. 350
   12.3 Critical phenomena: the Ising model ................... 352
   12.4 Renormalization with Monte Carlo simulation ........... 355
   12.5 Crossover: the Kondo problem .......................... 357
   12.6 Quantum lattice renormalization ....................... 360
   12.7 Density matrix renormalization ........................ 364
   Exercises .................................................. 367

References .................................................... 369
Index ......................................................... 381

Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск | English]
  Пожелания и письма: www@prometeus.nsc.ru
© 1997-2017 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Tue Mar 15 11:04:34 2016. Размер: 10,177 bytes.
Посещение N 141 c 22.03.2016