| Unit I |
Laplace Transform |
8 |
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Laplace transform definition and their properties, transform of derivatives and integrals, evaluation of integrals by Laplace Transform, Laplace transforms of periodic function, Unit step function, Unit Impulse function, Inverse Laplace Transform and its properties, convolution theorem, applications of Laplace transforms to solve ordinary differential equations |
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| Unit II |
Fourier Transform |
8 |
|
Complex exponential form of Fourier series, Fourier integral theorem, Fourier Sine & Cosine integrals, Fourier transform, Fourier Sine and Cosine transforms and their inverses, Properties of Fourier Transform, Discrete Fourier Transform. Applications of Transforms to boundary value Problems |
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| Unit III |
Z-Transform |
8 |
|
Definition, properties of Z- Transforms, Inverse Z- Transform and relation between Z transform and Laplace Transform. Convolution Theorem, Application of Z-Transform to solve difference equations with constant coefficients |
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| Unit IV |
Numerical Solution of Equations |
8 |
|
Numerical solutions of algebraic and transcendental equations. Iteration method, Bisection method, Regula-Falsi method, Newton-Raphson’s method and their convergences, solution of system of linear equations by Gauss elimination method, gauss Jordan method, gauss Seidel iteration method |
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| Unit V |
Numerical Solution of Ordinary Differential Equations |
8 |
|
Picard’s method, Taylor series method, Euler’s method, Modified Euler’s method, Range’s method, Runge-Kutta fourth order method, Predicator–corrector methods, Milne’s method. Solution of Simultaneous first order and higher order differential equations |
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