B.E. Electronics Engineering (Part Time)Yeshwantrao Chavan College of Engineering
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UNIT-I: Laplace Transforms
Laplace Transforms and their simple properties, simple application for
Laplace Transforms to solve ordinary differential equation including
Simultaneous equations, solution of one-dimensional partial differential
Equation by transforms method.
UNIT-II: Complex Variables
Analytic function, Cauchy-Riemann condition, Conjugate function,
Singulaterities , integral theorem and integral formula (statement only),
Taylor’s Laurent’s theorem (statement only), Residue theorem, contour
UNIT-III: Calculus of Variations
Maxima and Minima of function’s, variations and its properties. Euler’s
equations, functional dependent on first and second order
Derivatives, simple application.
UNIT-IV: Fourier series and Signal Spectra
Introduction, the Fourier theorem, Evaluation of Fourier
Coefficient, consideration of symmetry, (odd, even, rotational),
Exponential form: Fourier series, Fourier integral theorem,
Fourier Transforms and continuous spectra
UNIT-V: Partial Differential Equation
Partial Differential Equation of first order First Degree
i.e. Langrage’s form, Linear , homogenous P.D.E. Of
nth order with constant coefficient, method of separation
of variables , Application of transmission lines.
Inverse of matrix by adjoint method and its use in solving
Simultaneous Equation, rank of matrix, consistency of
System of equation, inverse of matrix by partitioning
Method. Linear dependence, Linear and orthogonal transformations
Characteristics Equations, eigen values and eigen vectors.
Reduction to diagonal form, Cayley – Hamiltone theorem(without proof)
Statement and verification ,Syltestor theorem ,Association of matrices with
Linear differential equation of second order with constant coefficient.
Determination of largest eigen values and eigen vectors by integration