**CSR Institute Of Mathematics**

Gate Mathematics Coaching In Chandigarh:-At City Beautiful Chandigarh have been giving GATE Mathematics Coaching since 2008.We have Specialization in Mathematics. A large number of understudies have cleared the exam.

We provide the Best Coaching in GATE Mathematics.We Taking a Regular test to Enhance the performance level with the goal that they Qualify the Exams in Large Numbers.

## Gate Mathematics Coaching In Chandigarh

GATE Online Application Processing System (GOAPS) Website Opens |
Friday |
01^{st} September 2017 |

Last Date for Submission of (Online) Application (through Website) | Monday | 09^{th} October 201720:00 Hrs (IST) |

Last Date for Requesting Change of Examination City (an additional fee will be applicable) | Friday | 17^{th} November 2017 |

Admit Card will be available in the Online Application Portal (for printing) | Friday | 05^{th} January 2018 |

GATE 2018 ExaminationForenoon: 9:00 AM to 12:00 Noon Afternoon: 2:00 PM to 5:00 PM |
Saturday Sunday Saturday Sunday |
03^{rd} February 201804 ^{th} February 201810 ^{th} February 201811 ^{th} February 2018 |

Announcement of the Results in the Online Application Portal | Saturday | 17^{th} March 2018 |

**SYLLABUS FOR GENERAL APTITUDE (GA)**

**Verbal Ability:**

English grammar, sentence completion, verbal analogies, word groups, instructions, critical reasoning and verbal deduction.

**Numerical Ability:**

Numerical computation, numerical estimation, numerical reasoning and data interpretation. Mathematics (MA).

**Linear Algebra:**

Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

**Complex Analysis:**

Analytic functions, conformal mappings, bilinear transformations; complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle; Taylor and Laurent’s series; residue theorem and applications for evaluating real integrals.

**Real Analysis:**

Sequences and series of functions, uniform convergence, power series, Fourier series, functions of several variables, maxima, minima; Riemann integration, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss; metric spaces, completeness, Weierstrass approximation theorem, compactness; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, dominated convergence theorem.

**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, series solutions; Legendre and Bessel functions and their orthogonality.

**Group:**

Normal subgroups and homomorphism theorems, automorphisms; Group actions, Sylow’s theorems, and their applications; Euclidean domains, Principle ideal domains, and unique factorization domains. Prime ideals and maximal ideals in commutative rings; Fields, finite fields.

**Functional Analysis:**

Banach spaces, Hahn-Banach extension theorem, open mapping and closed graph theorems, the principle of uniform boundedness; Hilbert spaces, orthonormal bases, Riesz representation theorem, bounded linear operators.

**Numerical Analysis:**

Numerical solution of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed point iteration; interpolation: error of polynomial interpolation, Lagrange, Newton interpolations; numerical differentiation; numerical integration: Trapezoidal and Simpson rules, Gauss-Legendre quadrature, method of undetermined parameters; least square polynomial approximation; numerical solution of systems of linear equations: direct methods (Gauss elimination, LU decomposition); iterative methods (Jacobi and Gauss-Seidel); matrix eigenvalue problems: power method, numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler’s method, Runge-Kutta methods.

**Partial Differential Equations:**

Linear and quasi linear first order partial differential equations, a method of characteristics; second order linear equations in two variables and their classification; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations.

**Mechanics:**

Virtual work, Lagrange’s equations for holonomic systems, Hamiltonian equations.

**Topology:**

Basic concepts of topology, product topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

**Probability and Statistics:**

Probability space, conditional probability, Bayes theorem, independence, Random variables, joint and conditional distributions, standard probability distributions and their properties, expectation, conditional expectation, moments; Weak and strong law of large numbers, central limit theorem; Sampling distributions, UMVU estimators, maximum likelihood estimators, Testing of hypotheses, standard parametric tests based on normal, X2 , t, F – distributions; Linear regression; Interval estimation.

**Linear programming:**

Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, big-M and two-phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems, dual simplex method and its application in post optimality analysis; Balanced and unbalanced transportation problems, u -v method for solving transportation problems; Hungarian method for solving assignment problems.

**Calculus of Variation and Integral Equations:**

Variation problems with fixed boundaries; sufficient conditions for extremum, linear integral equations of Fredholm and Volterra type, their iterative solutions.

Gate Mathematics Coaching In Chandigarh Gate Mathematics Coaching In Chandigarh Gate Mathematics Coaching In Chandigarh

## Recent Comments