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Unit - 1 Linear Differential Equations (LDE) and Applications

Unit 1Linear Differential Equations LDE and Applications

1.1 LDE of nth order with constant coefficients

1.2 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 Modelling of Electrical circuits

Unit - 2 Laplace Transform

Unit – 2 Laplace Transform

2.1 Definition of LT inverse LT

2.2 Properties and theorems of LT

2.3 LT of standard functions

2.4 LT of some special functions viz. Periodic

2.5 Unit step function

2.6 Unit impulse function

2.7 Applications of LT for solving linear differential equations

Unit - 3 Fourier and Z-Transforms

Unit – 3Fourier and ZTransforms

3.1 Fourier Transform FT Complex exponential form of Fourier series

3.2 Fourier integral theorem

3.3 Fourier Sine Cosine integrals

3.4 Fourier transform

3.5 Fourier Sine and Cosine transforms and their inverses

3.6 Z Transform ZT Introduction

3.7 Definition

3.8 Standard properties

3.9 ZT of standard sequences and their inverses

3.10 Solution of difference equations

Unit - 4 Statistics and probability

Unit – 4Statistics and probability

4.1 Measures of central tendency

4.2 Measures of dispersion

4.3 Coefficients of variation

4.4 Moments Skewness and kurtosis

4.5 Correlation regression Reliability of regression estimates

4.6 Probability and Probability density functions

4.7 Probability distributions Binomial Poisson and Normal

4.8 Test of hypothesis Chisquare test.

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