MATHEMATICS-III (Aditya Publication)
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UNIT-I: Ordinary differential equations: Complete solution, Operator D, Rules for finding complementary function, the inverse operator, Rules for finding the particular integral, Method of variation of parameters, Cauchy’s and Legendre’s linear differential equations.
UNIT-II: Laplace Transform: Definition, standard forms, properties of Laplace transform, inverse Laplace transform, Initial and final value theorem, Convolution theorem, Laplace transform of impulse function, Unit step function, Laplace transforms of periodic function.
UNIT-III: a) Applications of Laplace Transform: Solution of Linear differential equations, Simultaneous differential equation by Laplace transform method. b) Fourier Transform: Definition, standard forms, Fourier transforms, properties of Fourier transforms, Convolution theorem, Fourier sine and Fourier cosine transforms and integrals, inverse Fourier transforms.
UNIT-IV: a) Partial differential equation of first order of following form:- (i) f (p,q) = 0; (ii) f (p,q,z) = 0; (iii) f (x, p) = g (y,q); (iv) Pp + Qq = R (Lagranges Form); (v) z = px + qy + f(p,q) (Clairauts form). b) Statistics Curve fitting: Least Square Method, Coefficient of Correlations, Lines of Regression.
UNIT-V: Complex Analysis: Functions of complex variables, Analytic function, Cauchy- conditions, Harmonic function, Harmonic conjugate functions, Milne’s Method, conformal mappings (translation, rotation, magnification and bilinear transformation), Expansion of function in Taylor’s and Laurent’s series.
UNIT–VI: Vector Calculus: Scalar and vector point functions, Differentiation of vectors, Curves in space, Gradient of a scalar point function, Directional derivatives, Divergence and curl of a vector point function and their physical meaning, expansion Formulae (without proof), line, surface, volume integrals, irrotational Solenoidal Vector fields.
|Category||Books - Engineering - Computer Science - Semester-III|
|Dimensions||10(l) * 1(w) *10(h) CM|