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Unit - 1 Linear Differential Equations (LDE) and Applications

1.1 LDE of nth order with constant coefficients1.2 Complementary Function Particular Integral

1.3 General method Short methods

1.4 Method of variation of parameters

1.5 Cauchy‟s and Legendre’s DE

1.6 Simultaneous and Symmetric simultaneous DE

1.7 Modeling of Electrical circuits

Unit - 2 Transforms

2.1 Fourier Transform FT Complex exponential form of Fourier series2.2 Fourier integral theorem

2.3 Fourier Sine Cosine integrals

2.4 Fourier transform

2.5 Fourier Sine and Cosine transforms and their inverses

2.6 Z Transform ZT Introduction

2.7 Definition

2.8 Standard properties

2.9 ZT of standard sequences and their inverses

2.10 Solution of difference equations

Unit - 3 Numerical Methods

3.1 Interpolation Finite Differences 3.2 Newton‟s and Lagrange‟s Interpolation formulae

3.3 Numerical Differentiation

3.4 Numerical Integration Trapezoidal and Simpson‟s rules

3.5 Bound of truncation error

3.6 Solution of Ordinary differential equations Euler‟s Modified Euler‟s RungeKutta 4th order methods and PredictorCorrector methods

Unit - 4 Vector Differential Calculus

4.1 Physical interpretation of Vector differentiation4.2 Vector differential operator and Gradient

4.3 Divergence Curl and Directional derivative of a vector

4.4 Solenoidal and Irrotattional derivative

4.5 Conservative fields

4.6 Scalar potential

4.7 Vector identities

Unit - 5 Vector Integral Calculus & Applications

5.1 Line5.2 Surface and Volume integrals

5.3 Workdone

5.4 Green‟s Lemma

5.5 Gauss‟s Divergence theorem Stoke‟s theorem

5.6 Applications to problems in Electromagnetic fields

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