# TANCET Syllabus for Engineering Mathematics All Branches Part 1

Tamil Nadu Common Entrance Test - Engineering Mathematics Syllabus

 Chapter I Determinants & Matrices 1 Eigenvalues & eigenvectors 2 Rank of the Matrix 3 Reduction of quadratic form to canonical form. 4 Solving system of equations Chapter II Calculus & Differential Equations 1 Jacobians 2 Maxima & Minima. Linear ordinary differential equations with constant coefficients 3 Partial derivatives 4 Simultaneous first order linear equations with constant coefficients. Formation of partial differential equation (PDE) 5 Solution of first order PDE 6 Solution of linear higher order PDE with constant coefficients. 7 Taylor’s expansion Chapter III Vector Calculus 1 Double,triple integrations & their applications 2 Gradient, Divergence, Curl and Laplacian 3 Green’s, Gauss divergence and Stroke’s theorem. Chapter IV Functions of Complex Variables & Complex Integration 1 Analytic functions 2 Bilinear transformation 3 Cauchy’s integral theorem & integral formula 4 Conformal Mapping 5 Residue theorem & its applications 6 Residues 7 Singularities 8 Taylor and Laurent Series Chapter V Transforms 1 Laplace Transform 2 Inverse transforms 3 Application to solution of linear ordinary differential equations with constant coefficients. Fourier integral theorem 4 Fourier transform pair 5 Sine and Cosine transforms. -transform 6 Inverse Z transform 7 Solution of difference equations using Z transform Chapter VII Numerical Methods 1 Interpolation & approximation 2 Numerical Differentiation & Integration 3 Solution of linear system by direct & iterative methods 4 Solving Ordinary Differential Equations. Chapter VIII Applied Probability 1 Correlation & Regression. 2 Covariance 3 Moment generating function & their properties. Two-Dimensional Random Variables 4 Moments 5 Probability & Random variables 6 Standard Discrete & Continuous distribution