SYLLABUS FOR THE POST OF PRINCIPAL ITI / ASSISTANT
                                   DIRECTOR (TRAINING) IN TAMIL NADU EMPLOYMENT AND
                                             TRAINING SERVICE (DEGREE STANDARD)
                                                                 SUBJECT CODE: 230
                             UNIT- I: MATHEMATICS
Matrices: Eigenvalues - Eigenvectors – Cayley – Hamilton theorem – Similar and
Orthogonal transformations – Reduction of a quadratic form to canonical form by
orthogonal transformation.
Ordinary Differential Equations: Order and degree – Types of Equations – Higher
order linear ODE with constant coefficients - Method of variation of parameters –
Cauchy’s and Legendre’s linear equations – Simultaneous first order linear equations
with constant coefficient.
Functions of Several Variables: Partial derivatives – Total derivatives – Euler’s
theorem – Implicit functions – Jacobians – Taylor’s theorem – Maxima and Minima.
Integration: Techniques of integration using integration by parts and Bernoulli’s
formula – Line, Surface and Volume Integrals – Change of order of integration.
Vector Calculus: Vectors and scalars – Directional derivatives – Gradient, Divergence
and Curl of vectors – Applications of Green’s theorem, Gauss divergence theorem and
Stoke’s theorem.
Complex Variables: Verification of Analyticity – Construction of Analytic functions –
Conformal Mappings – Bilinear transformations.
Complex Integration: Cauchy’s integral theorem – Cauchy’s fundamental theorem –
Cauchy’s residue theorem – Taylor’s theorem – Laurent’s series – Contour integration

(excluding poles on the real axis).

Laplace Transform: Existence of Laplace transform – Laplace transform of elementary
functions – Properties – Laplace transform of Periodic functions – Inverse Laplace
transform – Convolution theorem – Solution of linear second order ODE by Laplace
transform technique.

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