KIITEE Syllabus for Mathematics
Unit-I:Cauchy, application of first order differential equations (mixture problem, Newtonís law of cooling, orthogonal trajectory), different equation of first order, application to LCR circuits, application to free and forced vibration of Mass spring system, Linear differential equation of second order (homogeneous and non-homogeneous case).
Unit-II:Series Method: Ordinary and singular point Frobenious method, properties of power series, Besselís equation and properties of Besselís function, radius of convergence of power series, Gamma function, Legenderís equation and Legenderís polynomial, properties of Legenderís polynomial.
Unit-III:Inverse Laplace transform, application to solve differential and integral equations (initial value problem), shifting theorems, periodic functions, convolution, Laplace transforms of standard function, unit step function, differentiation and integration of transforms, transforms fo derivatives and integrals.
Unit-IV:Fourier series expansions of even and odd function, expansion of functions with finite discontinuities, periodic function, even and odd functions Eulerís formula, Fourier series.
Unit-V:Solution of homogeneous system of equation, norm and their product, eigen values and eigen vectors, orthogonal and projection matrix, types of matrices, application of eigen values and vectors to solve the system of homogeneous linear differential equation, algebra of matrices, consistency of the system of equations, solution of non-homogenous system of equations, rank, linear dependence and independence.
Unit-VI:Directional derivatives, line integral, curl, divergence, Greenís theorem, vector algebra, double integral, product of vectors, gradient, vector differential operator, vector differentiation.