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Table of Contents

Chapter 11 Introduction to Probability and Statistics... 381

Introduction, Simulations, Representation of Data, Tabular Representation of Data,

Arithmetic Mean or Sample Mean, Median, Mode and Percentiles, The Geometric and

Harmonic Mean, The Root Mean Square (RMS), Mean Deviation and Sample Variance,

Probability, Probability Fundamentals, Probability of anEvent, Conditional Probability,

Permutations, Combinations, Binomial Coefficients, Discrete and Continuous Probability

Distributions, Scaling, The Normal Distribution, Standardization, The Binomial Distribu-

tion, The Multinomial Distribution, The Poisson Distribution, The Hypergeometric Distri-

bution, The Exponential Distribution, The Gamma Distribution, Chi-Square Distribution,

Student’s t-Distribution, The F-Distribution, The Uniform Distribution, Confidence Inter-

vals, Least Squares Curve Fitting, Linear Regression, Monte Carlo Methods, Obtaining a

Uniform Random Number Generator, Linear Interpolation

Chapter 12 Introduction to more Advanced Material..... 449

An integration method, The use of integration to sum infiniteseries, Refraction through a

prism, Differentiation of Implicit Functions, one equationtwo unknowns, one equation three

unknowns, one equation four unknowns, one equation n-unknowns, two equations three

unknowns, two equations four unknowns, three equations fiveunknowns, Generalization,

The Gamma function, Product of odd and even integers, Various representations for the

Gamma function, Euler formula for the Gamma function, The Zeta function related to the

Gamma function, Product property of the Gamma function, Derivatives of lnΓ(z) , Taylor

series expansion for lnΓ(x+1), Another product formula, Use of differential equationsto find

series, The Laplace Transform, Inverse Laplace transformL−^1 , Properties of the Laplace

transform, Introduction to Complex Variable Theory, Derivative of a Complex Function,

Integration of a Complex Function, Contour integration, Indefinite integration, Definite

integrals, Closed curves, The Laurent series

Appendix A Units of Measurement................................ 510

Appendix B Background Material.................................. 512

Appendix C Table of Integrals....................................... 524

Appendix D Solutions to Selected Problems................... 578

Index.................................................. .......................... 619

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