Computational Physics: Problem Solving with Computers, 2nd EditionISBN: 9783527406265
616 pages
September 2007

From the reviews of the first edition:
"Landau and Paez's book would be an excellent choice for a course on computational physics which emphasizes computational methods and programming."  American Journal of Physics
1 Introduction 1
1.1 Computational Physics and Computational Science 1
1.2 How to Use this Book 3
2 Computing Software Basics 7
2.1 Making Computers Obey 7
2.2 Computer Languages 7
2.3 Programming Warmup 9
2.4 Shells, Editors, and Programs 12
2.5 Limited Range and Precision of Numbers 13
2.6 Number Representation 13
2.7 IEEE Floating Point Numbers 14
2.8 Over/Underflows Exercise 20
2.9 Machine Precision 21
2.10 Determine Your Machine Precision 23
2.11 Structured Program Design 24
2.12 Summing Series 26
2.13 Numeric Summation 26
2.14 Good and Bad Pseudocode 27
2.15 Assessment 27
3 Errors and Uncertainties in Computations 29
3.1 Living with Errors 29
3.2 Types of Errors 29
3.3 Model for Disaster: Subtractive Cancellation 31
3.4 Subtractive Cancellation Exercises 32
3.5 Model for Roundoff Error Accumulation 34
3.6 Errors in Spherical Bessel Functions (Problem) 35
3.7 Numeric Recursion Relations (Method) 35
3.8 Implementation and Assessment: Recursion Relations 37
3.9 Experimental Error Determination 39
3.10 Errors in Algorithms 39
3.11 Minimizing the Error 41
3.12 Error Assessment 42
4 ObjectOriented Programming: Kinematics 45
4.1 Problem: Superposition of Motions 45
4.2 Theory: ObjectOriented Programming 45
4.3 Theory: Newton's Laws, Equation of Motion 46
4.4 OOP Method: Class Structure 47
4.5 Implementation: Uniform 1D Motion, unim1d.cpp 48
4.6 Assessment: Exploration, shms.cpp 56
5 Integration 59
5.1 Problem: Integrating a Spectrum 59
5.2 Quadrature as Box Counting (Math) 59
5.3 Algorithm: Trapezoid Rule 61
5.4 Algorithm: Simpson's Rule 63
5.5 Integration Error 65
5.6 Algorithm: Gaussian Quadrature 66
5.6.1 Mapping Integration Points 68
5.6.2 Gauss Implementation 69
5.7 Empirical Error Estimate (Assessment) 71
5.8 Experimentation 72
5.9 Higher Order Rules 72
6 Differentiation 75
6.1 Problem 1: Numerical Limits 75
6.2 Method: Numeric 75
6.3 Forward Difference 75
6.4 Central Difference 76
6.5 Extrapolated Difference 77
6.6 Error Analysis 78
6.7 Error Analysis (Implementation and Assessment) 79
6.8 Second Derivatives 80
7 Trial and Error Searching 81
7.1 Quantum States in SquareWell 81
7.2 TrialandError Root Finding via Bisection Algorithm 83
7.2.1 Bisection Algorithm Implementation 84
7.3 NewtonRaphson Algorithm 84
8 Matrix Computing and ND Newton Raphson 89
8.1 Two Masses on a String 90
8.2 Classes of Matrix Problems 95
9 Data Fitting 111
9.1 Fitting Experimental Spectrum 111
9.2 Fitting Exponential Decay 120
9.3 Theory: Probability and Statistics 121
9.4 LeastSquares Fitting 124
9.5 Appendix: Calling LAPACK from C 132
10 Deterministic Randomness 137
10.1 Random Sequences 137
11 Monte Carlo Applications 145
11.1 A RandomWalk 145
11.2 Radioactive Decay 148
11.3 Implementation and Visualization 151
11.4 Integration by Stone Throwing 152
11.5 Integration by Rejection 153
11.6 HighDimensional Integration 155
11.7 Integrating Rapidly Varying Functions 157
12 Thermodynamic Simulations: Ising Model 165
12.1 Statistical Mechanics 165
12.2 An Ising Chain (Model) 166
12.3 The Metropolis Algorithm 169
13 Computer Hardware Basics: Memory and CPU 179
13.1 HighPerformance Computers 179
13.2 The Central Processing Unit 184
14 HighPerformance Computing: Profiling and Tuning 189
14.1 Rules for Optimization 189
14.2 Programming for Data Cache 203
15 Differential Equation Applications 207
15.1 UNIT I. Free Nonlinear Oscillations 207
15.2 Nonlinear Oscillator 208
15.3 Math: Types of Differential Equations 209
15.4 Dynamical Form for ODEs 212
15.5 ODE Algorithms 213
15.6 Solution for Nonlinear Oscillations 223
15.7 Extensions: Nonlinear Resonances, Beats and Friction 225
15.8 Implementation: Inclusion of TimeDependent Force 226
15.9 UNIT II. Balls, not Planets, Fall Out of the Sky 228
15.10 Theory: Projectile Motion with Drag 228
15.11 Exploration: Planetary Motion 231
16 Quantum Eigenvalues via ODE Matching 235
16.1 Theory: The Quantum Eigenvalue Problem 236
17 Fourier Analysis of Linear and Nonlinear Signals 245
17.1 Harmonics of Nonlinear Oscillations 245
17.2 Fourier Analysis 246
17.3 Summation of Fourier Series(Exercise) 250
17.4 Fourier Transforms 250
17.5 Discrete Fourier Transform Algorithm (DFT) 252
17.6 Aliasing and Antialiasing 257
17.7 DFT for Fourier Series 259
17.8 Assessments 260
17.9 DFT of Nonperiodic Functions (Exploration) 261
17.10 Model Independent Data Analysis 262
17.11 Assessment 264
18 Unusual Dynamics of Nonlinear Systems 267
18.1 The Logistic Map 267
18.2 Properties of Nonlinear Maps 269
18.3 Explicit Mapping Implementation 271
18.4 Bifurcation Diagram 272
18.5 Random Numbers via Logistic Map 275
18.6 Feigenbaum Constants 276
18.7 Other Maps 276
19 Differential Chaos in Phase Space 277
19.1 Problem: A Pendulum Becomes Chaotic (Differential Chaos) 277
19.2 Equation of Chaotic Pendulum 278
19.3 Visualization: PhaseSpace Orbits 282
19.4 Assessment: Fourier Analysis of Chaos 288
19.5 Exploration: Bifurcations in Chaotic Pendulum 290
19.6 Exploration: Another Type of PhaseSpace Plot 291
19.7 Further Explorations 291
20 Fractals 293
20.1 Fractional Dimension 293
20.2 The Sierpi ´ nski Gasket 294
20.3 Beautiful Plants 297
20.4 Ballistic Deposition 301
20.5 Length of British Coastline 303
20.6 Problem 5: Correlated Growth, Forests, and Films 306
20.7 Problem 7: Fractals in Bifurcation Graph 311
21 Parallel Computing 313
21.1 Parallel Semantics 314
21.2 Distributed Memory Programming 316
21.3 Parallel Performance 317
22 Parallel Computing with MPI 321
22.1 Running on a Beowulf 322
22.2 Running MPI 326
22.3 Parallel Tuning: TuneMPI.c 340
22.4 A String Vibrating in Parallel 342
22.5 Deadlock 346
22.6 Supplementary Exercises 348
22.7 List of MPI Commands 349
23 Electrostatics Potentials via Finite Differences (PDEs) 351
23.1 PDE Generalities 351
23.2 Electrostatic Potentials 353
23.3 Fourier Series Solution of PDE 354
23.4 Solution: Finite DifferenceMethod 357
23.5 Assessment via Surface Plot 362
23.6 Three Alternate Capacitor Problems 363
23.7 Implementation and Assessment 365
23.8 Other Geometries and Boundary Conditions 368
24 Heat Flow 369
24.1 The Parabolic Heat Equation 369
24.2 Solution: Analytic Expansion 370
24.3 Solution: Finite Time Stepping (Leap Frog) 371
24.4 von Neumann Stability Assessment 373
24.5 Assessment and Visualization 376
25 PDE Waves on Strings and Membranes 379
25.1 The Hyperbolic Wave Equation 379
25.2 Realistic 1DWave Exercises 391
25.3 Vibrating Membrane (2DWaves) 392
25.4 Analytical Solution 394
25.5 Numerical Solution for 2DWaves 396
26 Solitons; KdeV and SineGordon 399
26.1 Chain of Coupled Pendulums (Theory) 399
26.2 Wave Dispersion 400
26.3 Analytic SGE Solution 403
26.4 Numeric Solution: 2D SGE Solitons 403
26.5 2D Soliton Implementation 406
26.6 Visualization 408
26.7 Shallow Water (KdeV) Solitons 409
26.8 Theory: The Kortewegde Vries Equation 410
27 Quantum Wave Packets 417
27.1 TimeDependent Schrödinger Equation (Theory) 417
27.2 Wave Packets Confined to OtherWells (Exploration) 422
28 Quantum Paths for Functional Integration 427
28.1 Feynman's SpaceTime Propagation 427
29 Quantum Bound States via Integral Equations 443
29.1 MomentumSpace Schrödinger Equation 444
30 Quantum Scattering via Integral Equations 451
30.1 LippmannSchwinger Equation 451
A PtPlot: 2D Graphs within Java 461
B Glossary 467
C Fortran 95 Codes 479
D Fortran 77 Codes 513
E C Language Codes 547
References 583
Index 587
Manuel J. Páez, PhD, is a professor in the Department of Physics at the University of Antioquia in Medellín, Colombia. He teaches courses in computational physics, programming, and nuclear physics. He and Professor Landau have conducted pioneering computational investigations in the interactions of mesons and nucleons with nuclei.
Cristian C. Bordeianu received his physics degree from Bucharest University, Romania, and his M.Sc. degree in Computer Science from "A.I.Cuza" University in Jassy, Romania. He is currently completing work towards a Ph.D. degree in Nuclear Physics at Bucharest University. He has over ten years of experience in developing Computational Physics educational software for high schools and University curricula. His current research interests include chaotic dynamics in nuclear multifragmentation and plasma of quarks and gluons.
 Visualization (including free packages: ptPlot, penDx, Grace, Gnuplot)
 Wavelet Analysis and Filtering and Data Compression
 Molecular Dynamics
 Computational Fluid Dynamics (incl shock waves, solitons)
EXTENSIONS (ADDED TO CHAPTERS)
 IEEE floating point arithmetic
 Trial & Error Searching and Matrix Computing with Libraries
 Object Oriented Programming with Java (major extension)
 Additional PDE techniques: successive over relaxation, finite element methods, CrankNicholson, LaxWendroff
 ODEs with rk2, rk4, rk45 and projectiles with drag
 ShortTime Fourier Analysis, FFT, Fourier Filtering
 Nonlinear Dynamics of Coupled PredatorPrey Systems
 Waves on a Catenary

Provides all its codes in the Java language, whose compiler and development kit are available for free for essentially all operating systems

Contains a CD that provides many of the same codes in Fortran 95, Fortran 77, and C, for even more universal application, as well as MPI codes for parallel applications

Includes new materials on trialanderror search techniques, IEEE floating point arithmetic, probability and statistics, optimization and tuning in multiple languages, parallel computing with MPI, JAMA the Java matrix library, the solution of simultaneous nonlinear equations, cubic splines, ODE eigenvalue problems, and Java plotting programs.
(American Journal of Physics)
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Computational Physics: Problem Solving with Computers, 2nd Edition (US $170.00)
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