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Unit - 1 Linear differential equations and Applications

1.1 LDE of nth order with constant coefficient Complementary functions Particular integral1.2 The general method and Short methods

1.3 Methods of variation of parameters

1.4 Cauchy’s and Legendre’s Different1ial Equation

1.5 Simultaneous and symmetric simultaneous differential equations

1.6 Modelling of mass spring system free and forced damped and undamped systems

Unit - 2 Transforms

2.1 Laplace transform LT LT of standard functions2.2 Properties and theorem Inverse LT

2.3 Application of LT to solve LDE

2.4 Fourier transform FT Fourier integral theorem

2.5 Fourier transforms

2.6 Fourier sine cosine transforms Inverse Fourier transforms

Unit - 3 Statistics

3.1 Measure of central tendency3.2 Measures of dispersion

3.4 Moments Skewness and Kurtosis

3.5 Curve fitting of a straight line

3.6 Fitting Parabola and related curves

3.7 Correlation and regression

3.8 Reliability of regression estimates

Unit - 4 Probability & Probability distributions

4.1 Probability Theorems on Probability4.2 Bayes theorem

4.3 Random variables

4.4 Mathematical expectation

4.5 Probability distributions Binomial Poisson and Normal distributions

4.6 Test of hypothesis Chisquare test ttest

Unit - 5 Vector Calculus

5.1 Vector differentiation 5.3 Divergence curl and vector identities

5.4 Directional derivative

5.5 Solenoidal Irrotational field

5.6 Line surface Volume integrals

5.7 Green’s lemma

5.8 Gauss’s divergence theorem

5.9 Stoke’s theorem

Unit - 6 Applications of partial differential equations (PDE)

6.1 Basic concept modelling of vibrating string6.2 Solution of wave equations

6.3 One and twodimensional heat flow equations

6.4 Method of separation of variables

6.5 Use of Fourier series Solution of heat equation by Fourier transform

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