Mathematics-III1. Unit-1
2. Unit-2
3. Unit-3
Shared by: pravin shrivastava(CSIT)
5. Unit-5
|
Mathematics-III SyllabusUNIT - 1 FOURIER SERIES
Expansion of function as Fourier series, Change of interval, Even and odd functions, Half-range Fourier series, Practical harmonic analysis. UNIT – 2 LAPLACE TRANSFORM Laplace transform of elementary functions, Properties of Laplace transform, Laplace transform of derivatives and integrals, multiplication by tn and division by t, Laplace transform of periodic functions. Inverse Laplace transform, Convolution theorem, Application of Laplace transform to solutions of ordinary differential equations. UNIT - 3 THEORY OF COMPLEX VARIABLES Limit, Derivative and Analytic functions; Cauchy-Riemann equations and its applications to flow problems; Complex Integration: Line and Contour integral, Cauchy integral theorem and Integral formula; Taylor series, Laurent series; singularities; Poles and their orders and residues; Evaluation of real definite integrals. UNIT - 4 PARTIAL DIFFERENTIAL EQUATION Formation of partial differential equations, Equations solvable by direct integration, Lagrange’s linear equations, Homogeneous linear differential equations with constant coefficients, Non-homogeneous linear equations, Solution of partial differential equations by the method of separation of variables. UNIT - 5 RANDOM VARIABLES Discrete and continuous probability distributions, Mathematical expectation, Mean and Variance, Moments, Moment generating function, probability distribution, Binomial, Poisson and Normal distributions. |