| List of Figures | p. ix |
| Preface | p. xi |
| Integration | p. 1 |
| Classical Quadrature | p. 1 |
| Orthogonal Polynomials | p. 10 |
| Orthogonal Polynomials in the Interval -1 [less than or equal] x [greater than or equal] 1 | p. 10 |
| General Orthogonal Polynomials | p. 13 |
| Gaussian Integration | p. 14 |
| Gauss-Legendre Integration | p. 16 |
| Gauss-Laguerre Integration | p. 16 |
| Special Integration Schemes | p. 19 |
| Principal Value Integrals | p. 20 |
| Introduction to Monte Carlo | p. 27 |
| Preliminary Notions - - Calculating [pi] | p. 27 |
| Evaluation of Integrals by Monte Carlo | p. 29 |
| Techniques for Direct Sampling | p. 32 |
| Cumulative Probability Distributions | p. 33 |
| The Characteristic Function [straight phi](t) | p. 33 |
| The Fundamental Theorem of Sampling | p. 34 |
| Sampling Monomials 0 [less than or equal] x [greater than or equal] 1 | p. 35 |
| Sampling Functions 0 [less than or equal] x [greater than or equal infinity] | p. 37 |
| The Exponential Function | p. 37 |
| Other Algebraically Invertible Functions | p. 37 |
| Sampling a Gaussian Distribution | p. 40 |
| Brute-force Inversion of F(x) | p. 41 |
| The Rejection Technique | p. 42 |
| Sums of Random Variables | p. 43 |
| Selection on the Random Variables | p. 44 |
| The Sum of Probability Distribution Functions | p. 47 |
| Special Cases | p. 49 |
| The Metropolis Algorithm | p. 50 |
| The Method Itself | p. 50 |
| Why It Works | p. 53 |
| Comments on the Algorithm | p. 54 |
| Differential Methods | p. 61 |
| Difference Schemes | p. 61 |
| Elementary Considerations | p. 61 |
| The General Case | p. 62 |
| Simple Differential Equations | p. 64 |
| Modeling with Differential Equations | p. 68 |
| Computers for Physicists | p. 75 |
| Fundamentals | p. 76 |
| Representation of Negative Numbers | p. 77 |
| Logical Operations | p. 79 |
| Integer Formats | p. 80 |
| Fixed Point Lengths | p. 80 |
| Floating Point Formats | p. 81 |
| Some Practical Conclusions | p. 83 |
| The i80X86 Series | p. 84 |
| The Stack | p. 84 |
| Memory Addressing | p. 85 |
| Internal Registers of the CPU | p. 86 |
| Instructions | p. 87 |
| A Sample Program | p. 92 |
| The Floating Point Co-processor i8087 | p. 94 |
| Two Important Bottlenecks | p. 95 |
| Cray-1 S Architecture | p. 95 |
| Vector Operations and Chaining | p. 96 |
| Coding for Maximum Speed | p. 97 |
| Intel i860 Architecture | p. 98 |
| Multi-Processor Computer Systems | p. 102 |
| Amdahl's Law | p. 102 |
| Difficulties | p. 103 |
| One Practical Solution: Beowulf Clusters | p. 103 |
| Algorithm types | p. 105 |
| "100%" Algorithms | p. 105 |
| Semi-efficient Algorithms | p. 106 |
| Costly algorithms | p. 106 |
| A Parallel Recursive Algorithm | p. 108 |
| Linear Algebra | p. 115 |
| X[superscript 2] Analysis | p. 115 |
| Solution of Linear Equations | p. 117 |
| Gaussian Elimination | p. 117 |
| LU Reductions | p. 120 |
| Crout's LU Reduction | p. 122 |
| The Gauss-Seidel Method | p. 125 |
| The Householder Transformation | p. 127 |
| The Eigenvalue Problem | p. 130 |
| Coupled Oscillators | p. 130 |
| Basic Properties | p. 131 |
| The Power Method for Finding Eigenvalues | p. 132 |
| The Inverse Power Method | p. 133 |
| Tridiagonal Symmetric Matrices | p. 134 |
| The Role of Orthogonal Matrices | p. 138 |
| The Householder Method for Eigenvalues | p. 139 |
| The Lanczos Algorithm | p. 139 |
| Exercises in Monte Carlo | p. 147 |
| The Potential Energy of the Oxygen Atom | p. 147 |
| Oxygen Potential Energy with Metropolis | p. 151 |
| Radiation Transport | p. 153 |
| An Inverse Problem with Monte Carlo | p. 157 |
| Finite Element Methods | p. 161 |
| Basis Functions - One Dimension | p. 162 |
| Establishing the System Matrix | p. 164 |
| Model Problem | p. 165 |
| The "Classical" Procedure | p. 165 |
| The Galerkin Method | p. 166 |
| The Variational Method | p. 168 |
| Example One-dimensional Program | p. 169 |
| Assembly by Elements | p. 171 |
| Problems in Two Dimensions | p. 172 |
| Element Functions | p. 172 |
| Laplace's Equation | p. 174 |
| Digital Signal Processing | p. 181 |
| Fundamental Concepts | p. 181 |
| Sampling: Nyquist Theorem | p. 181 |
| The Fast Fourier Transform | p. 184 |
| Phase Problems | p. 189 |
| Chaos | p. 193 |
| Functional Iteration | p. 193 |
| Finding the Critical Values | p. 202 |
| The Schrodinger Equation | p. 209 |
| Removal of the Time Dependence | p. 209 |
| Reduction of the Two-body System | p. 210 |
| Expansion in Partial Waves | p. 211 |
| The Scattering Problem | p. 213 |
| The Scattering Amplitude | p. 215 |
| Model Nucleon-nucleon Potentials | p. 223 |
| The Off-shell Amplitude | p. 225 |
| A Relativistic Generalization | p. 231 |
| Formal Scattering Theory | p. 232 |
| Modeling the t-matrix | p. 233 |
| Solutions with Exponential Potentials | p. 235 |
| Matching with Coulomb Waves | p. 239 |
| Bound States of the Schrodinger Equation | p. 242 |
| Nuclear Systems | p. 244 |
| Physics of Bound States: The Shell Model | p. 244 |
| Hypernuclei | p. 247 |
| The Deuteron | p. 248 |
| The One-Pion-Exchange Potential | p. 251 |
| Properties of the Clebsch-Gordan Coefficients | p. 256 |
| Time Dependent Schrodinger Equation | p. 258 |
| The N-body Ground State | p. 269 |
| The Variational Principle | p. 270 |
| A Sample Variational Problem | p. 271 |
| Variational Ground State of the [superscript 4]He Nucleus | p. 274 |
| Variational Liquid [superscript 4]He | p. 278 |
| Monte Carlo Green's Function Methods | p. 281 |
| The Green's Function Approach | p. 282 |
| Choosing Walkers for MCGF | p. 289 |
| Alternate Energy Estimators | p. 290 |
| Importance Sampling | p. 292 |
| An Example Algorithm | p. 294 |
| Scattering in the N-body System | p. 295 |
| More General Methods | p. 299 |
| Divergent Series | p. 303 |
| Some Classic Examples | p. 303 |
| Generalizations of Cesaro Summation | p. 305 |
| Borel Summation | p. 307 |
| Borel's Differential Form | p. 307 |
| Borel's Integral Form | p. 309 |
| Pade Approximants | p. 311 |
| Scattering in the N-body System | p. 319 |
| Single Scattering | p. 319 |
| First Order Optical Potential | p. 322 |
| Calculating the Non-local Potential | p. 324 |
| Solving with a Non-local Potential | p. 328 |
| Double Scattering | p. 331 |
| Relation of Double Scattering to Coherence | p. 335 |
| Scattering from Fixed Centers | p. 336 |
| The Watson Multiple Scattering Series | p. 340 |
| The KMT Optical Model | p. 346 |
| Medium Corrections | p. 346 |
| Programs | p. 355 |
| Legendre Polynomials | p. 355 |
| Gaussian Integration | p. 356 |
| Spherical Bessel Functions | p. 359 |
| Random Number Generator | p. 362 |
| Index | p. 363 |
| Table of Contents provided by Ingram. All Rights Reserved. |
