# GATE 2021 Mathematics Syllabus (Released) – Get (MA) PDF Here

Latest Applications Open 2020: GATE 2021 Syllabus of Mathematics has been Released. GATE 2021 is a national level exam organized by IIT Bombay (IITB).

The Engineering Graduation Skill Test (GATE 2021) is organized for admission to PG courses in the field of engineering and technology, specifically ME / M.Tech.

The exam will be held on 5th, 6th, 7th And 12th, 13th & 14th February 2021. See here for complete information about the GATE 2021 Syllabus.

## GATE 2021 Mathematics Syllabus – PDF Released GATE 2021 Mathematics Syllabus has been Released. Click Here to Download Pdf.

## GATE 2021 Mathematics Syllabus

Latest Applications For Various UG & PG Courses Open 2020:

1. Manav Rachna University, Haryana – 2020 UG & PG Admission Open. Apply Now
2. Bennett University (Times Group), Admission Open for 2020. Apply Now
3. Chandigarh University, Punjab 2020 Admission Open for all Courses. Apply Now
4. MIT World Peace University, Admissions Open for All Courses 2019-20. Apply Now
5. St. Andrew’s Institute of Technology and Management, Admission open 2020. Apply Now

Calculus: Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property; Sequences and series, convergence; Limits, continuity, uniform continuity, differentiability, mean value theorems; Riemann integration, Improper integrals;

Functions of two or three variables, continuity, directional derivatives, partial derivatives, total derivative, maxima and minima, saddle point, method of Lagrange’s multipliers; Double and Triple integrals and their applications; Line integrals and Surface integrals, Green’s theorem, Stokes’ theorem, and Gauss divergence theorem.

Linear Algebra: Finite dimensional vector spaces over real or complex fields; Linear transformations and their matrix representations, rank and nullity; systems of linear equations, eigenvalues, and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization,

Jordan canonical form, symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal and unitary matrices; Finite dimensional inner product spaces, Gram- Schmidt orthonormalization process, definite forms.

Real Analysis: Metric spaces, connectedness, compactness, completeness; Sequences and series of functions, uniform convergence; Weierstrass approximation theorem; Power series; Functions of several variables: Differentiation, contraction mapping principle,

Inverse and Implicit function theorems; Lebesgue measure, measurable functions; Lebesgue integral, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem.

Complex Analysis: Analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem, maximum modulus principle, Morera’s theorem; zeros and singularities; Power series, a radius of convergence,

Taylor’s theorem and Laurent’s theorem; residue theorem and applications for evaluating real integrals; Rouche’s theorem, Argument principle, Schwarz lemma; conformal mappings, bilinear transformations.

Ordinary Differential equations: First order ordinary differential equations, existence and uniqueness theorems for initial value problems, linear ordinary differential equations of higher order with constant coefficients; Second-order linear ordinary differential equations with variable coefficients;

Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations, series solutions (power series, Frobenius method); Legendre and Bessel functions and their orthogonal properties; Systems of linear first-order ordinary differential equations.

Algebra: Groups, subgroups, normal subgroups, quotient groups, homomorphisms, automorphisms; cyclic groups, permutation groups, Sylow’s theorems, and their applications;

## Also, Check Below-

Latest Applications For Various UG & PG Courses Open 2020:

1. Manav Rachna University, Haryana – 2020 UG & PG Admission Open. Apply Now
2. Bennett University (Times Group), Admission Open for 2020. Apply Now
3. Chandigarh University, Punjab 2020 Admission Open for all Courses. Apply Now
4. MIT World Peace University, Admissions Open for All Courses 2019-20. Apply Now
5. St. Andrew’s Institute of Technology and Management, Admission open 2020. Apply Now

Rings, ideals, prime and maximal ideals, quotient rings, unique factorization domains, Principle ideal domains, Euclidean domains, polynomial rings, and irreducibility criteria; Fields, finite fields, field extensions.

Functional Analysis: Normed linear spaces, Banach spaces, Hahn-Banach theorem, open mapping, and closed graph theorems, the principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, Riesz representation theorem.

Numerical Analysis: Numerical solutions of algebraic and transcendental equations: bisection, secant method, Newton-Raphson method, fixed-point iteration; Interpolation: error of polynomial interpolation, Lagrange and Newton interpolations; Numerical differentiation;

Numerical integration: Trapezoidal and Simpson’s rules; Numerical solution of a system of linear equations: direct methods (Gauss elimination, LU decomposition), iterative methods (Jacobi and Gauss-Seidel); Numerical solution of initial value problems of ODEs: Euler’s method, Runge-Kutta methods of order 2.

Partial Differential Equations: Linear and quasi-linear first-order partial differential equations, method of characteristics; Second-order linear equations in two variables and their classification; Cauchy, Dirichlet, and Neumann problems;

Solutions of Laplace and wave equations in two-dimensional Cartesian coordinates, interior and exterior Dirichlet problems in polar coordinates; Separation of variables method for solving wave and diffusion equations in one space variable; Fourier series and Fourier transform and Laplace transform methods of solutions for the equations mentioned above.

Topology: Basic concepts of topology, bases, subbases, subspace topology, order topology, product topology, metric topology, connectedness, compactness, countability and separation axioms, Urysohn’s Lemma.

Linear Programming: Linear programming problem and its formulation, convex sets and their properties, graphical method, basic feasible solution, simplex method, two-phase methods; infeasible and unbounded LPP’s, alternate optima; Dual problem and duality theorems; Balanced and unbalanced transportation problems, Vogel’s approximation method for solving transportation problems; Hungarian method for solving assignment problems.

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NMAT    Manav Rachna University MIT WPU

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