B.Tech. - AGRICULTURAL ENGINEERING Syllabus
B.Tech. - AGRICULTURAL ENGINEERING Syllabus I Year I – Semester (HS103) ENGINEERING MATHEMATICS – I L T P To C 3 1 - 4 4 UNIT – I Matrices : Matrices, Rank of a matrix, Solutions of system of linear equations, Gauss- Jordan, Gauss Elimination, Eigen values, Eigen vectors, Cayley-Hamilton theorem - Applications, Diagonalisation of a matrix. UNIT - II Ordinary Differential Equations: Revision of integral formulae, Formation of ordinary differential equations, Differential equations of first order and first degree – linear, Bernoulli and exact. Applications to Newton’s Law of cooling, Law of natural growth and decay, Orthogonal trajectories.Non-homogeneous linear differential equations of second and higher order with constant coefficients with RHS term of the type e, Sin ax, Cos ax, polynomials in x, method of variation of parameters UNIT – III Frobenius Series Solution: Frobenius series solution of differential equations (constant and variable coefficients) UNIT – IV Laplace Transformations : Definitions and properties, Laplace transform of standard functions, Inverse transform, first shifting Theorem, Transforms of derivatives and integrals, Unit step function, second shifting theorem, Dirac’s delta function, Convolution theorem, Differentiation and integration of transforms, Application of Laplace transforms to ordinary differential equations. UNIT - V Numerical Methods: Solutions of Algebraic and Transcendental equations: Bisection method, Regula-Falsi method, Newton-Raphson method, Numerical solutions of algebraic system of equations by Gauss-Siedel method. Interpolation: Errors in polynomial interpolation, Finite differences, Forward, backward and central differences, Newton’s formulae for interpolation, Central difference interpolation formulae, Gauss and Bessel central difference formulae, interpolation with unevenly spaced points, Lagrange’s interpolation formula. Curve fitting by least squares method, solving differential equations by numerical methods – Euler’s, Modified Eulers, RK method.
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