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Description of  TB Engineering Mathematics, Edition-2nd

SYLLABUS- ENGINEERING MATHEMATICS-I, Unit –1: Differential Calculus-I Successive Differentiation, Leibnitz’s theorem, Limit, Continuity and Differentiability of functions of several variables, Partial derivatives, Euler’s theorem for homogeneous functions, Total derivatives, Change of variables, Curve tracing: Cartesian and Polar coordinates. Unit–2: Differential Calculus-II Taylor's and Maclaurin's Theorems, Expansion of function of several variables, Jacobian, Approximation of errors, Extrema of functions of several variables, Lagrange’s method of multipliers ( Simple applications). Unit–3: Matrix Algebra Types of Matrices, Inverse of a matrix by elementary transformations, Rank of a matrix (Echelon & Normal form), Linear dependence, Consistency of linear system of equations and their solution, Characteristic equation, Eigen values and Eigen vectors, Cayley-Hamilton Theorem, Diago-nalization, Complex and Unitary Matrices and its properties. Unit–4: Multiple Integrals Double and triple integrals, Change of order of integration, Change of variables, Application of integration to lengths, Surface areas and Volumes, Cartesian and Polar coordinates. Beta and Gamma functions, Dirichlet’s integral and applications. Unit–5: Vector Calculus Point function, Gradient, Divergence and Curl of a vector and their physical interpretations, Vector identities, Tangent and Normal, Directional derivatives. Line, Surface and Volume integrals, Applications of Green’s, Stoke ’s and Gauss divergence theorems (without proof).