# Engineering Mathematics - Iii

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Linear Differential Equations (LDE)General order LDE. Solution of order LDE with constant coefficients. PI by variation of parameters. Cauchy s and Legendre s DE. Solution of simultaneous and symmetric simultaneous DE.Applications of DEApplications of LDE to problems on mass spring systems with coupled masses, equivalent electrical circuits. Solution of partial differential equations (PDE)(1) = , (2) and (3) by separating variables only. Applications of PDE to problems of mechanical and allied engineering.Matrices : Modal matrix, Normal modes of vibration characteristic equations and eigen values.TransformsLaplace Transform (LT) : Definition, Inverse LT, Properties and theorems (without proof). LT and inv-LT of elementary standard functions. Solution of differential equations using LT.Fourier Transform (FT) : Fourier integral theorem. Sine and Cosine integrals. Fourier Transform, Fourier Cosine Transform, Fourier Sine Transforms and their inverses. Application of FT to problems on diffusion equation.Statistics and ProbabilityMean, Mode, Median. Standard deviation, Variance, Coefficient of variation, Moments, Skewness and Kurtosis. Correlation and Regression, Reliability of regression estimates.Probability, Theorems and properties, Probability distributions viz. Binomial, Poisson, Normal, Hyper geometric, Chi square. Tests of hypothesis, Decision and quality control.Vector CalculusVector differentiation and its physical interpretation, Radial, Transverse, Tangential and Normal components of velocity and acceleration. Vector differential operation, Gradient, Divergence and Curl. Directional derivative. Vector identities.Vector AnalysisLine, Surface and Volume integrals. Work done. Conservative, Irrotational and Solenoidal fields, Scalar potential. Gauss s, Stoke s and Green s theorems (without proofs). Applications to problems in Fluid mechanics, Continuity equations, Stream lines, Equations of motion, Bernoulli s equations.5.22 begins to move with an initial conditions Assuming there is not friction, determine subsequent motion. [7 Marks] malt; = 1 k2 = m2 = 1 Fig. 5.22 2. The mass system in Fig. 5.23 begins to oscillate. Engineering Mathematics - 1 Matrices 5-31.

 Title : Engineering Mathematics - Iii Author : S. R. Bandewar S. D. Navare S. K. Kate, R. S. Acharya, A. R. Tambe Publisher : Technical Publications - 2006-01-01