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Full Description
Now in its second edition, Probabilistic Models for Dynamical Systems expands on the subject of probability theory. Written as an extension to its predecessor, this revised version introduces students to the randomness in variables and time dependent functions, and allows them to solve governing equations.Introduces probabilistic modeling and explores applications in a wide range of engineering fields Identifies and draws on specialized texts and papers published in the literatureDevelops the theoretical underpinnings and covers approximation methods and numerical methodsPresents material relevant to students in various engineering disciplines as well as professionals in the fieldThis book provides a suitable resource for self-study and can be used as an all-inclusive introduction to probability for engineering. It presents basic concepts, presents history and insight, and highlights applied probability in a practical manner. With updated information, this edition includes new sections, problems, applications, and examples. Biographical summaries spotlight relevant historical figures, providing life sketches, their contributions, relevant quotes, and what makes them noteworthy. A new chapter on control and mechatronics, and over 300 illustrations rounds out the coverage.
Contents
Introduction ApplicationsUnitsOrganization of the TextQuotesProblemsEvents and Probability SetsProbability SummaryQuotesProblemsRandom Variable Models Probability Distribution FunctionProbability Density FunctionProbability Mass FunctionMathematical ExpectationMean ValueUseful Continuous Probability Density FunctionsDiscrete Density FunctionsMoment-Generating FunctionTwo Random VariablesSummaryQuotesProblemsFunctions of Random Variables Exact Functions of One VariableFunctions of Two or More Random VariablesApproximate AnalysisMonte Carlo MethodsSummaryQuotesProblemsRandom Processes Basic Random Process DescriptorsEnsemble AveragingStationarityCorrelations of DerivativesFourier Series and Fourier TransformsHarmonic ProcessesPower SpectraNarrow- and Broad-Band ProcessesInterpretations of Correlations and SpectraSpectrum of DerivativeFourier Representation of a Stationary ProcessSummaryQuotesProblemsSingle Degree-of-Freedom Vibration Motivating ExamplesNewton's Second LawFree Vibration With No DampingHarmonic Forced Vibration With No DampingFree Vibration with Viscous DampingForced Harmonic VibrationImpulse ExcitationArbitrary LoadingFrequency Response FunctionSDOF: The Response to Random LoadsResponse to Two Random LoadsSummaryQuotesProblemsMulti Degree-of-Freedom Vibration Deterministic VibrationResponse to Random LoadsPeriodic StructuresInverse VibrationRandom EigenvaluesSummaryQuotesProblemsContinuous System Vibration Deterministic Continuous SystemsThe Eigenvalue ProblemDeterministic VibrationRandom Vibration of Continuous SystemsBeams with Complex LoadingSummaryQuotesProblemsReliability IntroductionFirst Excursion FailureOther Failure LawsFatigue Life PredictionSummaryQuotesProblemsNonlinear and Stochastic Dynamic Models The Phase PlaneStatistical Equivalent LinearizationPerturbation MethodsThe Mathieu EquationThe van der Pol EquationMarkov Process-Based ModelsSummaryQuotesProblemsNon-stationary Models Envelope Function ModelNon-stationary GeneralizationsPriestley's ModelOscillator ResponseMulti Degree-of-Freedom Oscillator ResponseNonstationary and Nonlinear OscillatorSummaryQuotesProblemsMonte Carlo Methods IntroductionRandom Number GenerationJoint Random NumbersError EstimatesApplicationsSummaryQuotesProblemsFluid-Induced Vibration Ocean Currents and WavesFluid Forces in GeneralExamplesAvailable Numerical CodesSummaryQuotesProbabilistic Models in Controls and Mechatronic Systems Concepts of Deterministic SystemsConcepts of Stochastic SystemsFiltering of Random SignalsWhite Noise FiltersStochastic System ModelsThe Kalman FilterAdditional IssuesSummaryQuotesIndex
