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ANALYSIS
Unit-1 1. METRIC SPACE 1-42 Metric and Metric Space 1; Quasi-Metric Space 5; Pseudo-Metric Space 5; Distance between Point and Set 6; Distance between Two Sets 6; Diameter of a Set 7; Some Important Inequalities 7; Product 11; Finite Product in General 12; Product of the Metric Spaces 13; Open Sphere 18; Open Disk (in Real Plane) 18; Open Disk (in Complex Plane) 18; Neighbourhood of a Point 18; Limit Point of a Set 18; Derived Set 19; Interior Point 19; Open Set 19; Closed Sphere 21; Closed Disk (in Real Plane) 21; Closed Disk (in Complex Plane) 21; Open and Closed Balls in RK 21; Convexity in RK 21; Closed Set 22; Closure of a Set 26; Interior of a Set 29; Exterior of a Set 29; Boundary Poi...
ABSTRACT ALGEBRA, DIFFERENTIAL EQUATION & FOURIER SERIES
ABSTRACT ALGEBRA UNIT-I 1. Group Automorphism, Inner Automorphism, Group of Automorphisms 1-22 Introduction 1; Homomorphism of Group 1; Types of Homomorphism 1; Kernel of a Homomorphism 3; Some Theorems (Properties of Group Homomorphism) 3; Isomorphism of Groups 3; Fundamental Theorem of Homomorphism of Groups 3; More Properties of Group Homomorphism 4; Automorphism of a Group 4; Inner Automorphism 8; Theorem 4; Definition of Inner Automorphism 8; Centre of a Group 9; Group of Automorphisms 12; Group of Automorphisms of a Cyclic Group 14. 2. Cayley's Theorem 23-32 Permutation Groups and Transformations 23; Equality of Two Permutations 24; Identity Permutations 24; Cayley’s Theorem for Fini...
VECTOR CALCULUS, GEOMETRY AND DIFFERENCE EQUATION
UNIT I Vector triple product. Product of four Vectors. Vector differentiation. Gradient, divergence and curl. Solenoidal and irrotational vector field. UNIT II Double integration. Properties of double integration. Iterated integral. Change of order of Integration. Transformation of double integral in polar form. UNIT III Spheres, Plane section of a sphere. Intersection of two sphere. Sphere through a given circle cone. Equation of cone with Vertex at origin. Right circular cone. Right circular cylinder. UNIT IV Formation of difference equation. Order of difference equation. Linear difference equation. Homogeneous linear equation with constant coefficient. Non homogeneous linear equation. Particular integrals.
