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Monday, February 4, 2013

Tancet 2014 Syllabus for MATHEMATICS TANCET 2013-2014 -

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Tancet 2013 Syllabus for MATHEMATICS TANCET 2013-2014  -


Tancet 2013 Syllabus for 

M.E./ M.Tech./ M.Arch./ M.Plan TANCET 2013 SYLLABUS TIME DURATION-2 Hours  
The question paper will have three parts.
Part-I and Part-II are compulsory and under Part-III the candidates
have to choose any one section out of 14 based on his/her


PART 2 BASIC ENGINEERING & SCIENCES (Common to all Candidates) 

(i) Algebra
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.

(ii) Analysis
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, produt topology, connectedness, ompactness, 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.

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