SYLLABUS ENGINEERING MATHEMATICS-III - (207006) Credits Examination Scheme [Marks] Th : 03 In Sem : 30 Marks End Sem : 70 Marks Unit I : Linear Differential Equations (LDE) and Applications LDE of 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. Modeling of Electrical circuits. (Chapters - 1, 2) Unit II : Laplace Transform (LT) Definition of LT, Inverse LT, Properties & theorems, LT of standard functions, LT of some special functions viz. Periodic, Unit Step, Unit Impulse. Applications of LT for solving Linear differential equations. (Chapter - 3) Unit III : Fourier and Z - transforms Fourier Transform (FT) : Complex exponential form of Fourier series, Fourier integral theorem, Fourier Sine & Cosine integrals, Fourier transform, Fourier Sine & Cosine transforms and their inverses. Z - Transform (ZT) : Introduction, Definition, Standard properties, ZT of standard sequences and their inverses. Solution of difference equations. (Chapters - 4, 5) Unit IV : Statistics and Probability Measures of central tendency, Measures of dispersion, Coefficient of variation, Moments, Skewness and Kurtosis, Correlation and Regression, Reliability of Regression estimates. Probability, Probability density function, Probability distributions : Binomial, Poisson, Normal, Test of hypothesis : Chi-square test. (Chapters - 6, 7) Unit V : Vector Calculus Vector differentiation, Gradient, Divergence and Curl, Directional derivative, Solenoidal and Irrotational fields, Vector identities. Line, Surface and Volume integrals, Green’s Lemma, Gauss’s Divergence theorem and Stoke’s theorem. (Chapter - 8) Unit VI : Complex Variables Functions of a Complex variable, Analytic functions, Cauchy-Riemann equations, Conformal mapping, Bilinear transformation, Cauchy’s integral theorem, Cauchy’s integral formula and Residue theorem. (Chapters - 9, 10)