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 


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