Syllabus Engineering Mathematics III [207001] Credits Examination scheme 04 In semester exam : 30 Marks End semester exam : 70 Marks Term Work : 25 Marks 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 problems on bending of beams, whirling of shafts and mass spring systems. Unit II : Numerical Methods Numerical solutions of system of linear equations : Gauss elimination method, Cholesky, Jacobi and Gauss-Seidel methods. Numerical solutions of ordinary differential equations: Euler’s, Modified Euler’s, Runge-Kutta 4th order and Predictor-Corrector methods. Unit III : Statistics and Probability Measures of central tendency, Standard deviation, 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, t-test. Unit IV : Vector Differential Calculus Physical interpretation of Vector differentiation, Vector differential operator, Gradient, Divergence and Curl, Directional derivative, Solenoidal, Irrotational and Conservative fields, Scalar potential, Vector identities. Unit V : Vector Integral Calculus and Applications Line, Surface and Volume integrals, Work-done, Green’s Lemma, Gauss’s Divergence theorem, Stoke’s theorem. Applications to problems in Fluid Mechanics, Continuity equations, Streamlines, Equations of motion, Bernoulli’s equation. Unit VI : Applications of Partial Differential Equations (PDE) Basic concepts, modeling of Vibrating String, Wave equation, One and two dimensional Heat flow equations, method of Separation of variables, use of Fourier series, Applications of PDE to problems of Civil and allied Engineering.
