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ABSTARCT ALGEBRA & LINEAR ALGEBRA
Unit-I 0. Historical Background .... 1-4 1. Groups and Their Basic Properties .... 1-65 2. Subgroups .... 66-80 3. Cyclic Groups .... 81-93 4. Coset Decomposition, Lagrange’s and Fermat’s Theorem .... 94-113 5. Normal Subgroups .... 114-125 6. Quotient Groups .... 126-131 Unit-II 7. Homomorphism and Isomorphism of Groups, Fundamental Theorem of Homomorphism .... 132-151 8. Transformation and Permutation Group Sn (n < 5), Cayley’s Theorem .... 152-186 9. Group Automorphism, Inner Automorphism, Group of Automorphisms .... 187-206 Unit-III 10. Definition and Basic Properties of Rings, Subrings .... 207-232 11. Ring Homomorphism, Ideals, Quotient Ring .... 233-259 12. Polynomial Ringh .......
INTEGRAL TRANSFORM
Unit-I Laplace Transform : 1.1 Linearity property 1.2 Existence theorem 1.3 Shifting theorem 1.4 Change of scale property 1.5 Laplace transforms of derivatives and integrals 1.6 Differentiation and integration of the Laplace transforms 1.7 Multiplication and division by 't' 1.8 Periodic function Unit-II Inverse Laplace Transform : 2.1 Linearity property 2.2 Shifting theorem 3.3 Change of scale property 2.4 Inverse Laplace transforms of derivatives and integrals 2.5 Multiplication and division by powers of p 2.6 Convolution theorem 2.7 Heaviside expansion theorem Unit-III Application of Laplace Transform : 3.1 Solution of ordinary differential equations with constant coefficients 3.2 Solution of ordinary differential equations with variable coefficients Unit-IV Fourier Transform : 4.1 Linearity property 4.2 Shifting theorem 4.3 Change of scale property 4.4 Modulation 4.5 Convolution theorem 4.6 Fourier transform of derivatives 4.7 Relations between Fourier transform and Laplace transform 4.8 Parseval's identity for Fourier transform 4.9 Solution of differential equations using Fourier transform
UNIFIED MATHEMATICS ADVANCED CALCULUS
MATHEMATICS, GANIT, RAM PRASAD, RPP UNFIED RP HARI KISHAN, THAKUR
DISCRETE MATHEMATICS
RAM PRASAD, RP UNIFIED, RPP, GANIT, THAKUR KISHAN
MATHEMATICS
MATHEMATICS, GANIT, RAM PRASAD, RPP UNIFIED, RP GANIT, THAKUR KISHAN
UNIFIED MATHEMATICS ABSTRACT ALGEBRA
MATHEMATICS, GANIT, RAM PRASAD, RP UNIFIED, RPP
MATHEMATICS - CALCULUS AND DIFFERENTIAL EQUATIONS
MATHEMATICS, GANIT, RP UNIFIED, RAM PRASAD RPP
UNIFIED MATHEMATICS
MATHEMATICS, MATHS, RAM PRASAD, RP UNIFIED, RPP, THAKUR, KISHAN, GANIT
ELEMENTS OF DISCRETE MATHEMATICS
1. Indian Logic 1-5 2. Relations, Equivalence Classes and Partition of a set 6-25 3. Partial Order Relation and Lattices 26-48 4. Boolean Algebra and Boolean Function 49-89 5. Graphs and Sub-graphs 90-111 6. Walk, Paths, Circuits, Weighted Graphs and Shortest Path 112-150 7. Trees and its Simple Properties 151-189 8. Matrix Representation of a Graph, Cut Sets and Planar Graph 190-216
CALCULUS & DIFFERENTIAL EQUATIONS
Contents Chapter Page No. Calculus and Diffeential Equations Unit-I 0.Historical Background....i-xvi 1.Successive Differentiation and Leibnitz’s Theorem....1-33 2.Maclaurin and Taylor Series Expansions....34–51 3.Partial Differentiation....52-74 4.Euler’s Theorem on Homogeneous Functions....75-98 5.Asymptotes....99-127 Unit-II 6.Curvature....128-162 7.Tests for Concavity and Convexity, Points of Inflexion....163-173 8.Mulitiple Points, Tracing of Curves in Cartesian and Polar Coordinates....174-205 Unit-III 9.Integration of Irrational, Algebraic and Transcendental Functions....206-276 10.Definite Integrals....277-302 11.Reduction Formulae....303-339 12.Double and Triple Integrals, Diri...
