TANCET Mathematics Syllabus.
TANCET Mathematics Syllabus 2014 TamilNadu CET i.e TANCET is an exam conducted by Anna University. TANCET means (Tamil Nadu Common Entrance Test) 2014 for admission to MBA, MCA, M.E./M.Tech/M.Arch/M.Plan programme in Tamil Nadu. The test is conducted at various centers through out the country.
TANCET Mathematics Syllabus
Algebra: Group, subgroups, Normal subgroups, Quotient Groups, Homomorphisms, Cyclic Groups, permutation Groups, Cayley’s Theorem, Rings, Ideals, Integral Domains, Fields, Polynomial Rings. Linear Algebra: Finite dimensional vector spaces, Linear transformations – Finite dimensional inner product spaces, self-adjoint and Normal linear operations, spectral theorem, Quadratic forms.
Real Analysis: Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima, multiple integrals, line, surface and volume integrals, theorems of Green, Strokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness.
Complex Analysis: Analytic functions, conformal mappings, bilinear transformations, complex integration: Cauchy’s integral theorem and formula, Taylor and Laurent’s series, residue theorem and applications for evaluating real integrals.
(iii) Topology and Functional Analysis
Topology: Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma, Tietze extension theorem, metrization theorems, Tychonoff theorem on compactness of product spaces.
Functional Analysis: Banach spaces, Hahn-Banach theorems, open mapping and closed graph theorems, principle of uniform boundedness; Hilbert spaces, orthonormal sets, Riesz representation theorem, self-adjoint, unitary and normal linear operators on Hilbert Spaces.
(iv) Differential and Integral Equations
Ordinary Differential Equations: First order ordinary differential equations, existence and uniqueness theorems, systems of linear first order ordinary differential equations, linear ordinary differential equations of higher order with constant coefficients; linear second order ordinary differential equations with variable coefficients, method of Laplace transforms for solving ordinary differential equations.
Partial Differential Equations: Linear and quasilinear first order partial differential equations, method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems, Green’s functions; solutions of Laplace, wave and diffusion equations using Fourier series and transform methods. Calculus of Variations and Integral Equations: Variational problems with fixed boundaries;
sufficient conditions for extremum, Linear integral equations of Fredholm and Volterra type, their iterative
solutions, Fredholm alternative.
(v) Statistics & Linear Programming
Statistics: Testing of hypotheses: standard parametric tests based on normal, chisquare, t and Fdistributions. Linear Programming: Linear programming problem and its formulation, graphical method, basic feasible solution, simplex method, big-M and two phase methods. Dual problem and duality theorems, dual simplex method. Balanced and unbalanced transportation problems, unimodular property and u-v method for solving transportation problems. Hungarian method for solving assignment problems.