Topics in CUET PG Mathematics Syllabus 2025 - Algebra, Real Analysis, Integral Calculus

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CUET PG important chapters

Algebra

Real Analysis

Complex Analysis

Integral Calculus

Differential Equations

Vector Calculus

Linear Programming

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CUET PG Maths chapter

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Real Analysis

Sequences and series of real numbers. Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and

conditional convergence; Tests of convergence for series of positive terms-comparison test, ratio test, root

test, Leibnitz test for convergence of alternating series.

Functions of one variable: limit, continuity, differentiation, Rolle's Theorem, Cauchy’s Taylor's theorem. Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series.

Functions of two real variable: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

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Complex Analysis

Functions of a complex Variable, Differentiability and analyticity, Cauchy Riemann

Equations, Power series as an analytic function, properties of line integrals, Goursat Theorem, Cauchy

theorem, consequence of simply connectivity, index of a closed curves.

Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, Fundamental theorem of Algebra, Harmonic functions.

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Integral Calculus

Integration as the inverse process of differentiation, definite integrals and their

properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

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Differential Equations

Ordinary differential equations of the first order of the form y'=f(x,y).

Bernoulli's equation, exact differential equations, integrating factor, Orthogonal trajectories,

Homogeneous differential equations-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy-Euler equation.

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Vector Calculus

Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line

integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.