9789630576154

Introduction to the Monte-Carlo Method

by
  • ISBN13:

    9789630576154

  • ISBN10:

    9630576155

  • Format: Paperback
  • Copyright: 1999-07-01
  • Publisher: Intl Specialized Book Service Inc
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Table of Contents

Introduction
9(2)
Probability
11(25)
Basic Concepts of Probability
11(2)
Probability and Frequency
11(1)
Law of Addition of Probabilities
12(1)
Law of Multiplication of Probabilities
12(1)
Conditional Probability
12(1)
Random Variables
13(5)
Discrete Random Variable
13(2)
Continuous Random Variable
15(3)
Probability Distributions
18(14)
Joint Distribution of Two Random Variables
18(1)
Composition of Distributions
19(1)
Uniform Distribution
20(1)
Binomial Distribution (Bernoulli Distribution)
20(3)
Poisson Distribution
23(3)
Exponential Distribution
26(1)
Gamma Distribution
27(2)
Gaussian Distribution
29(1)
χ2 Distribution
30(1)
Student's t Distribution
31(1)
Central Limit Theorem
32(1)
Measured Data
33(3)
Mean value
33(1)
Empirical Variance
34(1)
Expectation Value of Empirical Variance
35(1)
Random Numbers
36(6)
True Random Numbers
36(1)
Pseudorandom Numbers
37(3)
J. von Neumann's Mid-Square Method
38(1)
Multiplicative Congruent Random Number Generator
39(1)
Uniform Random Number Generator
40(1)
Quasi Random Numbers
40(2)
Richtmyer formula
41(1)
Van der Corput formula
41(1)
Transformations
42(2)
General Method
43(1)
Test of Random Numbers
44(1)
General Method
44(1)
A Useful Test
44(1)
Monte-Carlo Techniques
45(37)
Discrete Random Variable
45(1)
Continuous Random Variable
45(17)
Analytical Method
47(1)
Linear Interpolation
48(1)
Distribution Given in Histogram
49(9)
Linear Interpolation in Two Dimensions
58(1)
J. von Neumann's Acceptance-Rejection Method
59(1)
Importance Sampling Method
60(2)
Two-Dimensional Acceptance-Rejection Method
62(1)
Algorithms
62(20)
Uniform Distribution
62(1)
Uniform Distribution on Interval
63(1)
Uniform Distribution in Square
64(1)
Uniform Distribution in Circle
64(1)
Uniform Distribution in Sphere
65(1)
Random Direction on Plane
66(1)
Sine and Cosine of Random Angle
67(1)
Random Directions
68(2)
Binomial Distribution
70(2)
Poisson Distribution
72(2)
Exponential Distribution
74(1)
Gamma Distribution
75(1)
Gaussian Distribution
76(4)
χ2 Distribution
80(1)
Student's t Distribution
81(1)
Monte-Carlo Integration
82(4)
Crude Monte-Carlo
83(1)
Acceptance-Rejection Method
83(1)
Control Variate Monte-Carlo
84(1)
Stratified Sampling
84(1)
Antithetic Variate
84(2)
Surface and Volume Calculations
86(2)
Simulation Examples
88(22)
Radioactive Decay
88(1)
Propagation of Neutrons
89(6)
Simulation of KOS→ &mgr;+ &mgr;- Decay
95(5)
Quality of Equipments
100(1)
Reliability of Equipments
100(1)
Queues
101(4)
Roundabout
105(5)
Error of Monte-Carlo Calculations
110(1)
Role of Monte-Carlo Method in Analysis of Measurements
111(2)
APPENDIX 113(49)
A. Program Listing of KOS→ &mgr;+ &mgr;- Decay
115(11)
B. Display
126(1)
B.1. Quasy 3D Display
126(1)
C. Histogram
127(1)
D. Gamma Function
128(1)
E. Binary Search
129(2)
E.1. Precision of binary division
129(2)
F. The Function URAND
131(2)
G. Spline Interpolation
133(4)
H. Calculus
137(8)
H.1. Vectors
137(1)
H.1.1. Scalar Product of Vectors
138(1)
H.1.2. Vector Product of Vectors
138(1)
H.2. Combinatorics
138(1)
H.2.1. Permutations
138(1)
H.2.2. Variations
139(1)
H.2.3. Combinations
139(1)
H.3. Linear Equation System
139(1)
H.3.1. Matrix Algebra
140(1)
H.3.2. Inverse Matrix (Gauss-Jordan Elimination)
141(1)
H.3.3. Determinants
141(1)
H.4. Differential Calculus
142(2)
H.5. Integral Calculus
144(1)
I. Function Minimization
145(2)
I.1. Minimization with Golden Section
146(1)
J. Error Propagation
147(1)
K. Straight Line Fit
148(1)
L. Standard Deviation
149(1)
M. Optics
150(3)
M.1. Propagation of Electromagnetic Radiation
150(1)
M.1.1. Reflection
151(1)
M.1.2. Refraction
152(1)
N. Coordinate Transformations
153(2)
N.1. Parallel Translation
153(1)
N.2. Rotation
153(1)
N.3. Rectangular and Polar Coordinate Systems
154(1)
N.3.1. Transformation from Rectangular into Polar Coordinate System
154(1)
N.3.2. Transformation from Polar into Rectangular Coordinate System
154(1)
O. Glossary
155(7)
References 162

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