An introduction to computational physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 2. ed., repr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 385 S. graph. Darst. |
| ISBN: | 0521825695 9780521825696 9780521532761 |
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| 245 | 1 | 0 | |a An introduction to computational physics |c Tao Pang |
| 250 | |a 2. ed., repr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XV, 385 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Physics |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804138135172415488 |
|---|---|
| adam_text | 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
VII
viii
Contents
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
Contents ¡x
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
Contents
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
|
| adam_txt |
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
VII
viii
Contents
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
Contents ¡x
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
Contents
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 |
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| edition | 2. ed., repr. |
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| index_date | 2024-07-02T22:29:22Z |
| indexdate | 2024-07-09T21:23:22Z |
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| isbn | 0521825695 9780521825696 9780521532761 |
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| physical | XV, 385 S. graph. Darst. |
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| spelling | Pang, Tao Verfasser aut An introduction to computational physics Tao Pang 2. ed., repr. Cambridge [u.a.] Cambridge Univ. Press 2008 XV, 385 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computerphysik - Lehrbuch Datenverarbeitung Mathematische Physik Mathematical physics Numerical calculations Physics Data processing Physics Methodology Computer (DE-588)4070083-5 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Computerphysik (DE-588)4273564-6 gnd rswk-swf Computerphysik (DE-588)4273564-6 s DE-604 Physik (DE-588)4045956-1 s Computer (DE-588)4070083-5 s 1\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016814721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pang, Tao An introduction to computational physics Computerphysik - Lehrbuch Datenverarbeitung Mathematische Physik Mathematical physics Numerical calculations Physics Data processing Physics Methodology Computer (DE-588)4070083-5 gnd Physik (DE-588)4045956-1 gnd Computerphysik (DE-588)4273564-6 gnd |
| subject_GND | (DE-588)4070083-5 (DE-588)4045956-1 (DE-588)4273564-6 |
| title | An introduction to computational physics |
| title_auth | An introduction to computational physics |
| title_exact_search | An introduction to computational physics |
| title_exact_search_txtP | An introduction to computational physics |
| title_full | An introduction to computational physics Tao Pang |
| title_fullStr | An introduction to computational physics Tao Pang |
| title_full_unstemmed | An introduction to computational physics Tao Pang |
| title_short | An introduction to computational physics |
| title_sort | an introduction to computational physics |
| topic | Computerphysik - Lehrbuch Datenverarbeitung Mathematische Physik Mathematical physics Numerical calculations Physics Data processing Physics Methodology Computer (DE-588)4070083-5 gnd Physik (DE-588)4045956-1 gnd Computerphysik (DE-588)4273564-6 gnd |
| topic_facet | Computerphysik - Lehrbuch Datenverarbeitung Mathematische Physik Mathematical physics Numerical calculations Physics Data processing Physics Methodology Computer Physik Computerphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016814721&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pangtao anintroductiontocomputationalphysics |