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Summary
Summary
This second edition increases the universality of the previous edition by providing all its codes in the Java language, whose compiler and development kit are available for free for essentially all operating systems. In addition, the accompanying CD 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. The book also includes new materials on trial-and-error 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.
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
Author Notes
Rubin H. Landau, PhD, is a professor in the Department of Physics at Oregon State University in Corvallis. He teaches courses in computational physics, helps direct the Northwest Alliance for Computational Science and Engineering, and has been using computers in theoretical physics research for the past 30 years. The author of more than 70 refereed publications, he has also authored the books Quantum Mechanics II, A Scientist's and Engineer's Guide to Workstations and Supercomputers, and the first edition of Computational Physics, all of them available from Wiley.
Manuel J. P�ez, PhD, is a professor in the Department of Physics at the University of Antioquia in Medell�n, 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.
Reviews 1
Choice Review
Landau and Paez provide a systematic treatment of computational methods used in physics, suitable for individuals with backgrounds in mathematics, computer programming, and physics at the advanced undergraduate level or higher. The book is broad in scope; it begins with a chapter on programming techniques and then treats the types of errors present in computational solutions. Following an introduction to the methods of numerical integration, 30 chapters present numerous numerical methods and applications. Among the topics and methods discussed are data fitting, differentiation, integration, differential equations, linear and nonlinear partial differentiation equations, matrices, and Monte Carlo methods. A sampling of the areas of physics includes radioactive decay, oscillations, quantum physics, nonlinear oscillations and systems, chaos, thermodynamics, fractals, heat flow, electrostatics, and waves. Chapters on computer hardware, high-performance computing, and parallel computing are included. A floppy disk with source code in Fortran and C provides many sample programs. Quite useful for upper-division undergraduates, graduates, faculty, and professionals. D. S. Fielder SUNY College at Oneonta
Table of Contents
| 1 Introduction |
| 1.1 Computational Physics and Computational Science |
| 1.2 How to Use this Book |
| 2 Computing Software Basics |
| 2.1 Making Computers Obey |
| 2.2 Computer Languages |
| 2.3 Programming Warmup |
| 2.4 Shells, Editors, and Programs |
| 2.5 Limited Range and Precision of Numbers |
| 2.6 Number Representation |
| 2.7 IEEE Floating Point Numbers |
| 2.8 Over/Underflows Exercise |
| 2.9 Machine Precision |
| 2.10 Determine Your Machine Precision |
| 2.11 Structured Program Design |
| 2.12 Summing Series |
| 2.13 Numeric Summation |
| 2.14 Good and Bad Pseudocode |
| 2.15 Assessment |
| 3 Errors and Uncertainties in Computations |
| 3.1 Living with Errors |
| 3.2 Types of Errors |
| 3.3 Model for Disaster: Subtractive Cancellation |
| 3.4 Subtractive Cancellation Exercises |
| 3.5 Model for Roundoff Error Accumulation |
| 3.6 Errors in Spherical Bessel Functions (Problem) |
| 3.7 Numeric Recursion Relations (Method) |
| 3.8 Implementation and Assessment: Recursion Relations |
| 3.9 Experimental Error Determination |
| 3.10 Errors in Algorithms |
| 3.11 Minimizing the Error |
| 3.12 Error Assessment |
| 4 Object-Oriented Programming: Kinematics |
| 4.1 Problem: Superposition of Motions |
| 4.2 Theory: Object-Oriented Programming |
| 4.3 Theory: Newton's Laws, Equation of Motion |
| 4.4 OOP Method: Class Structure |
| 4.5 Implementation: Uniform 1D Motion, unim1d.cpp |
| 4.6 Assessment: Exploration, shms.cpp |
| 5 Integration |
| 5.1 Problem: Integrating a Spectrum |
| 5.2 Quadrature as Box Counting (Math) |
| 5.3 Algorithm: Trapezoid Rule |
| 5.4 Algorithm: Simpson's Rule |
| 5.5 Integration Error |
| 5.6 Algorithm: Gaussian Quadrature |
| 5.7 Empirical Error Estimate (Assessment) |
| 5.8 Experimentation |
| 5.9 Higher Order Rules |
| 6 Differentiation |
| 6.1 Problem 1: Numerical Limits |
| 6.2 Method: Numeric |
| 6.3 Forward Difference |
| 6.4 Central Difference |
| 6.5 Extrapolated Difference |
| 6.6 Error Analysis |
| 6.7 Error Analysis (Implementation and Assessment) |
| 6.8 Second Derivatives |
| 7 Trial and Error Searching |
| 7.1 Quantum States in SquareWell |
| 7.2 Trial-and-Error Root Finding via Bisection Algorithm |
| 7.2 1 Bisection Algorithm Implementation |
| 7.3 Newton-Raphson Algorithm |
| 8 Matrix Computing and N-D Newton Raphson |
| 8.1 Two Masses on a String |
| 8.2 Classes of Matrix Problems |
| 9 Data Fitting |
| 9.1 Fitting Experimental Spectrum |
| 9.2 Fitting Exponential Decay |
| 9.3 Theory: Probability and Statistics |
| 9.4 Least-Squares Fitting |
| 9.5 Appendix: Calling LAPACK from C |
| 10 Deterministic Randomness |
| 10.1 Random Sequences |
| 11 Monte Carlo Applications |
| 11.1 A RandomWalk |
| 11.2 Radioactive Decay |
| 11.3 Implementation and Visualization |
| 11.4 Integration by Stone Throwing |
| 11.5 Integration by Rejection |
| 11.6 High-Dimensional Integration |
| 11.7 Integrating Rapidly Varying Functions |
| 12 Thermodynamic Simulations: Ising Model |
| 12.1 Statistical Mechanics |
| 12.2 An Ising Chain (Model) |
| 12.3 The Metropolis Algorithm |
| 13 Computer Hardware Basics: Memory and CPU |
| 13.1 High-Performance Computers |
| 13.2 The Central Processing Unit |
| 14 High-Performance Computing: Profiling and Tuning |
| 14.1 Rules for Optimization |
| 14.2 Programming for Data Cache |
| 15 Differential Equation Applications |
| 15.1 UNIT I. Free Nonlinear Oscillations |
| 15.2 Nonlinear Oscillator |
| 15.3 Math: Types of Differential Equations |
| 15.4 Dynamical Form for ODEs |
| 15.5 ODE Algorithms |
| 15.6 Solution for Nonlinear Oscillations |
| 15 |
