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