# Engineering Mathematics - III for SPPU 19 Course (SE - IV - MECH. - 207002)

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Unit I Linear Differential Equations (LDE) and Applications LDE of nth order with constant coefficients, Complementary Function, Particular Integral, General method, Short methods, Method of variation of parameters, Cauchy’s and Legendre’s DE, Simultaneous and Symmetric simultaneous DE. Modelling of Mass-spring systems, Free & Forced damped and undamped systems. (Chapters - 1, 2) Unit II Transforms Laplace Transform (LT) : LT of standard functions, properties and theorems, Inverse LT, Application of LT to solve LDE. Fourier Transform (FT) : Fourier integral theorem, Fourier transform, Fourier sine & cosine transforms, Inverse Fourier Transforms. (Chapters - 3, 4, 5) Unit III Statistics Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Curve fitting : fitting of straight line, parabola and related curves, Correlation and Regression, Reliability of Regression Estimates. (Chapter - 6) Unit IV Probability and Probability Distributions Probability, Theorems on Probability, Bayes Theorem, Random variables, Mathematical Expectation, Probability distributions: Binomial, Poisson, Normal, Test of Hypothesis : Chi-Square test, t-test. (Chapter - 7) Unit V Vector Calculus Vector differentiation, Gradient, Divergence and Curl, Directional derivative, Solenoidal & Irrotational fields, Vector identities. Line, Surface and Volume integrals, Green’s Lemma, Gauss’s Divergence theorem and Stoke’s theorem. (Chapters - 8, 9) Unit VI Applications of Partial Differential Equations (PDE) Basic concepts, modelling of Vibrating String, Solution of Wave equation, One and two dimensional Heat flow equations, Method of separation of variables, use of Fourier series. Solution of Heat equation by Fourier transforms. (Chapter - 10)

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