Probabilistic Models in Engineering and Science Book

INTRODUCTION Applications Units Organization of the Text Problems

EVENTS AND PROBABILITY Sets Probability Concluding Summary Problems

RANDOM VARIABLE MODELS Probability Distribution Function Probability Density Function Mathematical Expectation Variance

USEFUL PROBABILITY DENSITIES Two Random Variables Concluding Summary Problems

FUNCTIONS OF RANDOM VARIABLES Exact Functions of One Variable Functions of Two or More RVs General Case Approximate Analysis Monte Carlo Method Concluding Summary Problems The Standard Normal Table

RANDOM PROCESSES Basic Random Process Descriptors Ensemble Averaging Stationarity Derivatives of Stationary Processes Fourier Series and Fourier Transforms Harmonic Processes Power Spectra Fourier Representation of a Random Process Borgman's Method of Frequency Discretization Concluding Summary Problems

SINGLE DEGREE OF FREEDOM DYNAMICS Motivating Examples Deterministic SDoF Vibration SDoF: The Response to Random Loads Response to Two Random Loads Concluding Summary Problems

MULTI DEGREE OF FREEDOM VIBRATION Deterministic Vibration Response to Random Loads Periodic Structures Inverse Vibration Random Eigenvalues Concluding Summary Problems

CONTINUOUS SYSTEM VIBRATION Deterministic Continuous Systems Sturm-Liouville Eigenvalue Problem Deterministic Vibration Random Vibration of Continuous System Beams with Complex Loading Concluding Summary Problems

RELIABILITY Introduction First Excursion Failure Fatigue Life Prediction Concluding Summary Problems NONLINEAR DYNAMIC MODELS Examples of Nonlinear Vibration Fundamental Nonlinear Equations Statistical Equivalent Linearization Perturbation Methods The van der Pol Equation Markov Process Based Models Concluding Summary Problems

NONSTATIONARY MODELS Some Applications Envelope Function Model Nonstationary Generalizations Priestley's Model SDoF Oscillator Response Multi DoF Oscillator Response Nonstationary and Nonlinear Oscillator Concluding Summary Problems

THE MONTE CARLO METHOD Introduction Random Number Generation Joint Random Numbers Error Estimates Applications Concluding Summary Problems

FLUID INDUCED VIBRATION Ocean Currents and Waves Fluid Forces - In General Examples Available Numerical Codes Index