## Wednesday, January 23, 2013

Latest: TNEA 2014 Engineering Application Status, Counselling Date, Rank List
TANCET ME/MTECH SYLLABUS PART 1 2013
Expected Syllabus for Tancet 2013 Exam

PART – I
ENGINEERING MATHEMATICS (Common to all Candidates)

i)      Determinants and Matrices : Solving system of equations – Rank of the Matrix – Eigenvalues
and eigenvectors – Reduction of quadratic form to canonical form.

ii)     Calculus and Differential Equations : Partial derivatives – Jacobians – Taylor’s expansion -
Maxima and Minima. Linear ordinary differential equations with constant coefficients – Simultaneous first
order linear equations with constant coefficients. Formation of partial differential equation (PDE) -
Solution of first order PDE – Solution of linear higher order PDE with constant coefficients.

iii)  Vector Calculus : Double and triple integrations and their applications – Gradient, Divergence, Curl
and Laplacian – Green’s, Gauss divergence and Stroke’s theorem.

iv)  Functions of Complex Variables and Complex Integration : Analytic functions – Conformal
Mapping – Bilinear transformation – Cauchy’s integral theorem and integral formula – Taylor and Laurent
Series – Singularities – Residues – Residue theorem and its applications.

v)    Transforms : Laplace Transform – Inverse transforms – Application to solution of linear ordinary
differential equations with constant coefficients. Fourier integral theorem – Fourier transform pair – Sine
and Cosine transforms. -transform – Inverse Z-transform – Solution of difference equations using Z-
transform.

vi)      Numerical Methods : Solution of linear system by direct and iterative methods – Interpolation
and approximation – Numerical Differentiation and Integration – Solving Ordinary Differential Equations.

vii)        Applied Probability : Probability and Random variables – Standard Discrete and Continuous
distribution – Moments – Moment generating function and their properties. Two-Dimensional Random
Variables – Covariance – Correlation and Regression.