Credits: 3 (3-0-0)
Description
Ordinary Differential Equation: Second order ODEs, Method of Undetermined Coefficients, Variation of Parameters, Strum-Liouville eigenvalue problem, Difference equation. Partial Differential Equation: Classification of PDEs, Heat, Wave and Laplace Equations, Separation of variables to solve PDEs. Fourier Transform: Fourier sine transform, Fourier cosine Transform, Technique for solving ODEs and PDEs. Probability Theory: Axioms of probability, Conditional probability, Random variable, Uncertainty in engineering system, Discrete and Continuous distributions, Distribution function, Joint probability distribution, Moments, Covariance, Correlation coefficient. Stochastic Processes: Definition of Stochastic process, Stochastic FE model, Stationary process, Markov chain, Poisson process.