- 1:Introduction to Numerical Integration
- 2:NI.1: Newton-Cotes Formulae
- 3:Linear Equations for Coefficients
- 4:Examples of Newton Cotes Rules I
- 5:Examples of Newton Cotes Rules II
- 6:Formulae for Examples: Trapezoidal and Simpson's Rules
- 7:Summary of Newton Cotes Rules
- 8:Errors in Newton Cotes Formulae
- 9:Use of High Order Newton Cotes
- 10:Strategies for Manipulating Integrals before using Standard Numerical Integration
- 11:Criteria for Choosing Manipulation
- 12:Dangers in Integrating Non-Analytic Functions
- 13:Why Do We Have Problems with Non-Analytic Functions?
- 14:Combining Analytic and Numerical Integration
- 15:Cunning Choice of Weight Functions
- 16:Change of Variable Before Numerical Integration---I
- 17:Change of Variable Before Numerical Integration---II
- 18:How Do You Choose Correct Strategy?
- 19:Hybrid Strategy Example (continued)
- 20:NI.2: Romberg or Adaptive Integration
- 21:NI.3: Gaussian Integration
- 22:Some Mathematics Underlying Gaussian Integration
- 23:More Mathematics Deriving Gaussian Integration Formulae
- 24:Basic Gaussian Integration
- 25:When Should You Use Gaussian?
- 26:Three Choices of in Numerical Integration
- 27:NI.4: Parallel Computing and Integration
- 28:Issues for Parallel Computing
- 29:Two-Dimensional Integrals
- 30:NI.5: Monte Carlo Integration
- 31:Basic Formulation of Integral as a Mean (Expectation Value)
- 32:Basic Monte Carlo Approach to Integration
- 33:Why Monte Carlo Methods Are Best in Multidimensional Integrals
- 34:Best Multidimensional Integration Formulae
- 35:Distribution of Points in Two-dimensional Integral Done by Newton-Cotes Style Formulae
- 36:Distribution of Points in Two-dimensional Integral Done by Monte Carlo
- 37:Use of Bounding Boxes to Calculate --- I
- 38:Use of Bounding Boxes to Calculate --- II
- 39:Use of Bounding Boxes in Complicated Geometries --- I
- 40:Use of Bounding Boxes in Complicated Geometries --- II
- 41:IMPORTANCE Sampling Basic Theory
- 42:Choice of Importance Sampling Weight Function --- I
- 43:Choice of Importance Sampling Weight Function --- II
- 44:Monte Carlo Approach to Discrete Integrals
- 45:Why Use Monte Carlo for Summations?
- 46:Example of using Monte Carlo for Summations
- 47:The Wrong Way to Perform Multiple Monte Carlo
- 48:Stock Market Example of Multiple Monte Carlos --- I
- 49:Stock Market Example of Multiple Monte Carlos --- II
- 50:Number of Points Needed in Joint Monte Carlo
- 51:Accept/Reject Method for Generating General Probability Distributions
- 52:Estimate of Maximum in Accept/Reject Method
- 53:Introduction to Metropolis Method
- 54:The Metropolis Procedure
- 55:Why Metropolis Method Works
- 56:Monte Carlo Examples Example 1: An Experimental Physics Application
- 57:A High Energy Experiment Scenario
- 58:An Experimental Physics Monte Carlo
- 59:Double Monte Carlo's Again --- I
- 60:Double Monte Carlo's Again --- II
- 61:A Monte Carlo Event
- 62:Uniform Weight Events
- 63:What Happens If You Miscalculate Maximum Weight in Accept/Reject Approach
- 64:Example 2: Parallel Computing for ``Event'' Monte Carlos
- 65:Example 3: Lattice Monte Carlo Theoretical Physics
- 66:Choice of Points in Lattice Monte Carlo
- 67:Pictorial View of Lattice Monte Carlo Integrands
- 68:Metropolis and Heat Bath Methods
- 69:Calculation of Observables
- 70:Example 4: Parallel Computing for Lattice Theory
- 71:A Problem Lattice Decomposed Onto a 64-node Machine Arranged as a Machine Lattice
- 72:The 16 Time and Eight Internal Gluon Degrees of Freedom

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