Advanced Engineering Mathematics

Advanced Engineering Mathematics Linear Algebra Vector spaces: Vector Spaces, Subspaces, Bases and Dimensions and related theorems.

Linear Transforms: Isomorphism, Homomorphism, Matrix representations, Linear Functionals, The Double Dual.

Concept of Random Variables Introduction, Distribution and Density faction, Specific Random Variables, Conditional Distributions, asymptotic approximations for binomial random variable, The Distributions, Mean and Variance, Moments generating functions.

Two Dimensional Random Variables Bivariate Distributions, One function of two random variables, Two function of two random variables, Joint Moments, Joint Characteristic Functions, Conditional Distributions, Conditional Expected Values, Sequence of Random Variables.

Concept of Stochastic Process System with Stochastic Inputs, The Power Spectrum, Discrete time Processes, Continuity, Differentiations and Integration, Shift Operators and Stationary Processes, Random Walks Poission Points and Shot Noise, Modulation, Bandlimited Processes and Sampling Theory.

Markov Process and Queuing Theory Introduction, Higher-Transition Probability and the Chapman-Kolmogorov Equation, Classification of States, Stationary Distributions and Limiting Probabilities, Transient States and Absorption Probabilities, Markov Process, Queuing Theory, Networks of Queues.