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

GATE 2019 Mathematics SyllabusGATE 2021 Syllabus of Mathematics has been Released. GATE 2021 is a national level exam organized by IIT DELHI.

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 the 1st week of February 2021. See here for complete information about the GATE 2021 Syllabus.

GATE 2021 Mathematics Syllabus – PDF Released

New GATE 2021 Mathematics Syllabus has been Released. Click Here to Download Pdf.

GATE 2021 Mathematics Syllabus

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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. Shiv Nadar University, Greater Noida, UP | Admission Open 2020. Apply Now
    2. Bennett University (Times Group), Admission Open for 2020. Apply Now
    3. Manav Rachna University, Haryana – 2020 UG & PG Admission Open. Apply Now
    4. Manipal University 2020 Admission Open For UG & PG Courses. Apply Now
    5. UPES, Dehradun Enroll Yourself for the Academic Year 2020. Apply Now
    6. LPU, Punjab Admissions 2020 Open | Secure Your Admission Online‎. Apply Now
    7. Pearl Academy No.1 Fashion School – Admissions Open for 2020 batch. Apply Now
    8. Amrita University, Admissions Open for BTech 2020. Apply Now
    9. Chandigarh University, Punjab 2020 Admission Open for all Courses. Apply Now
    10. Sharda University, Admission Open 2020, Few Days left. 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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