The exhaustive list of topics in Random Vibrations  in which we provide Help with Homework Assignment and Help with Project is as follows:

• Random vibrations & Failure Analysis.
• Random vibration & probabilistic modeling.
• Axioms of probability theory:
• Probability space.
• Random variables.
• Probability distributions and density functions of random variables.
• Joint and marginal distribuition.
• Density functions.
• Functions of random variables.
• Expectations and moments of random variables.
• Baye's theorem.
• Conditional random variables.
• Conditional expectations.
• Characteristic functions.
• Moment generating functions.
• Cumulants.
• Relationship between joint probability density functions and characteristic functions.
• Numerical issues.
• Covariance and independence.
• Sequences of random variables.
• Stochastic convergence.
• Limit theorems.
• Concepts of stochastic processes, probability distributions, moments, correlation and covariance functions.
• The power spectral density function.
• Stationarity and non-stationarity of stochastic processes, ergodicity of a stochastic process.
• Limits of a stochastic process.
• Continuity & differentiability.
• Stochastic derivatives and integrals.
• Special random processes -1: Gaussian random processes.
• Special random processes -2: Poisson processes and random pulses.
• Special random processes -3: Random walk & wiener processes.
• Special random processes -4: Markov processes.
• The Fokker-Planck-Kolmogorov equation.
• Stochastic calculus.
• Numerical simulation of random processes.
• Deterministic dynamics and impulse response functions of systems.
• System response to random excitations.
• Response to stationary & weakly stationary excitations.
• Delta-correlated excitations.
• Response to Gaussian excitations.
• Non-stationary excitations.
• Joint behavior of the time deriative and its response & Markov vector approach.
• Linear dynamics and harmonic transfer functions.
• Generalization to multi degree-of-freedom systems.
• State space formulation of equations of motion.
• The Fokker-Planck equation for linear systems.
• The Fokker-Planck equation for sdof systems.
• The Fokker-Planck equation for mdof systems.
• Methods for Numerical solutions for the FPK equation: finite difference.
• Methods for Numerical solutions for the FPK equation: finite element method.
• Numerical solutions for the FPK equation: Path integral method.
• Method of equivalent statistical linearization.
• State space moment and cumulant equations.
• Level crossings and the first passage time.
• Probability distribution of maxima & failure probability.
• Peak distributions & their applications.
• Envelope crossings and their distributions.
• Generralization to non-Gaussian processes
• Numerical evaluation of Rice's formula.