Tamil Nadu Common Entrance Test (TANCET) : Syllabus - Mathematics

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Tamil Nadu Common Entrance Test (TANCET)

Application Procedure

Syllabus

Exam Date 2024

Syllabus
Part -I : Engineering Mathematics
Part - II : Basic Engineering & Sciences
Part - III : 1) Civil Engineering & Geo Informatics | 2) Earth Science | 3) Mechanical, Automobile & Aeronautical Engineering | 4) Electrical & Electronics Engineering and Instrumentation Engineering | 5) Electronics & Communication Engineering | 6) Production & Industrial Engineering | 7) Computer Science & Engineering and Information Technology | 8) Chemical Engineering, Ceramic Technology & Biotechnology | 9) Textile Technology | 10) Leather Technology | 11) Architecture | 12) Physics & Material Science | 13) Mathematics | 14) Social Science

PART - III (13) 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 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, 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.