Solution to Engineering Mathematics-I (With Previous 10 Years Solved Paper) Strictly as per the latest syllabus prescribed by UPTU, Lucknow and Uttrakhand Technical Univresity, Dehradun

Leibnitz's theorem, Partial derivatives, Euler's theorem for homogeneous functions, Total derivatives, Change of variables, Curve tracing: Cartesian and Polar coordinates. Taylor's and Maclaurin's Theorems, Expansion of function of several variables, Jacobian, Approximation of errors. Double and triple integrals, Change of order of integration, Change of variables. Point function, Gradient, Divergence and Curl and their physical interpretations, Vector identities. Elementary row and column transformation rank of a matrix. Linear dependence, consistency of linear system of equations and their solution. Characteristic equation. Cayley-Hamilton theorem. Eigen values and Eigen vectors, diagonalization. Complex and unitary matrices.. Application of matrices to engineering problems.