**KU PGCET 2019 Notification M.Sc Maths Syllabus download**: Kakatiya University PGCET notification 2019 released. Candidates are suggested to check the KU PGCET 2019 Notification M.Sc Maths Syllabus before preparng for the exam. Here in this article candidates can check the information related to KU PGCET 2019 Syllabus.

## KU PGCET 2019 Notification M.Sc Maths Syllabus download

**MATHEMATICS / STATISTICS / APPLIED MATHEMATICS Syllabus pdf**

**KU PGCET 2019 Part - A (50 Marks)**

GROUP THEORY: Examples and elementary properties of groups - sub groups - Lagranges theorem - Normal sub-group - Homomorphism - Isomorphism - Automorphism - Kernal of Homomorphism - Cyclic groups - Permutation groups.

RINGS AND FIELDS: Definition and examples of rings and fields - Elementary properties of rings - Integral domains - Ilomomorphism - Fundamental theorem of homomorphism of rings - Ideals - Maximal ideals - Prime ideals - Principle ideals -Definition and examples of Euclidean rings.

REAL ANALYSIS: Sets of real numbers - Dedckind property • Bounded sets - Limit point ofa set. sequences - Convergence - Divergence - Bounded and Monotonic sequence - Cauchy's sequence - Convergence of series - Comparison test - Ratio test - Absolute and conditional convergence - Alternating series - Leibnitzs test.

LIMITS AND CONTINUITY: Limits of functions - Left hand limit - Right hand limit and limit of a function - Theorems on limits - Continuous and discontinuous functions - Removable continuity - Properties of continuous functions on a closed interval [a.b].

DIFFERENTIATION: Differentiability of function - Rolles. Lagranges and Cauchy's mean value theorems - Maclaurins expansion of functions.

INTEGRA TION: Riemann integrability of function - Properties of integral functions - Primitive - Fundamental theorem of integral calculus.

**KU PGCET 2019 Part - B (50 Marks)**

ELEMENTARY TRANSFORMATION: Reduction of matrix to the normal Iorrns > Rank of the matrix - Elementary Matrices - Computation of the inverse of matrix - system of linear equations and consistency - Characteristic equation - Caley-Hamilton theorem,

VECTOR CALCULUS: Vector differentiation - Differential operator - Gradient - Divergence Curl - Vector integration - Theorems of Gauss. Green and Stokes and problems related to them.

DIFFERENTIAL EQUATIONS: Differential equations of first order and first degree -Variable seperable - Homogeneous equations - Non-Ilomogeneous equations - Exact equations - Linear equations of first order and higher degrec equations - Second order equations with constant coefficient and variable coefficient. change of independent variable - Variation of parameters - Simultaneous differential equations.

VECTOR SPACES: Vector spaces - Sub spaces - Linear spaces - Linear independent - Linear dependent of vectors - Linear span - Basis - Dimension - Algebra of linear transformation _ Rank-Nullity theorem.

INNER PRODUCT SPACES: Definition and examples of inner product spaces - Orthonormal set of vectors - Scwartz iqequality - Bessel's inequality - Orthogonal complements - The adjoining. normal. self adjoint. unitary and orthogonal operators.

SOLID GEOMETRY: The plane - Equation of a plane. normal form. intercept form and passing through three points - Length of the perpendicular from a given point to a plane _ Bisectors of angle between plane - The equation of line - Shortest distance between two straight lines - Sphere - Cone - Cylinder.

MULTIPLE INTEGRA LS: The concept of plane curve - Line integrals - The area of a subset in a plane - Calculation of double integrals - Jordan curve - Area - Change of the order of integration.

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