Electronics & Telecommunication Engineering(4th Sem.)
Mathematics-IV__________________________________1. Unit-1
2. Unit-2
3. Unit-3
4. Unit-4
5. Unit-5
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Mathematics-IV SyllabusUNIT - 1 SERIES SOLUTION OF DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS Series solution of differential equations, The method of Frobenius, Bessel's differential equation, Bessel’s function of the First Kind - recurrence relations, generating function, orthogonality, Legendre's differential equation, Legendre’s polynomial - Rodrigue’s formula, generating function, recurrence relations, orthogonality. UNIT - 2 PARTIAL DIFFERENTIAL EQUATIONS: Formation, Solution of Lagrange's linear differential equation, homogeneous linear differential equation with constant coefficients, non-homogeneous linear differential equations, Method of separation of variables. UNIT - 3 APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS Initial & boundary value problems, Vibrations of a stretched string, D'Alembert's solution, Onedimensional heat flow, Transmission of signals along a cable - Telephone equation, Telegraph & radio equations, Vibrations of rectangular & circular membranes. UNIT - 4 Z - TRANSFORM Sequence, Basic operations on sequences, Definition of Z- Transform, Linearity, Change of scale & shifting properties, Z-transform of standard sequences, Inverse Z- Transform, Multiplication by n & division by n, Initial value & final value theorems, Convolution of sequences, Convolution theorem, Inverse Z- transform by partial fraction, power series and residue methods. Application to solution of difference equations. UNIT - 5 RANDOM VARIABLE & PROBABILITY DISTRIBUTIONS Random variable, Discrete & continuous probability distributions, Mathematical Expectation, Mean & variance, Moments & moment generating function, Probability distributions -Binomial, Poisson & Normal distributions. |
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