## Friday, January 24, 2014

### Tancet 2014 Syllabus for MATHEMATICS TANCET 2014-2015 - www.annauniv.edu

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### Tancet 2014 Syllabus for MATHEMATICS TANCET 2014-2015  - www.annauniv.edu

TANCET 2014 SYLLABUS FOR ME/M.TECH MATHEMATICS

Tancet 2013 Syllabus for
MATHEMATICS - TANCET 2014-2015

M.E./ M.Tech./ M.Arch./ M.Plan TANCET 2014 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
specialisation.

PART 2 BASIC ENGINEERING & SCIENCES (Common to all Candidates)
PART 3 MATHEMATICS

(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

(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.