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Sequence and its convergence (basic idea). Convergence of infinite series. Comparison test, ratio test root, test. Raabe’s test, Logarithmic ratio .... Read More
Sequence and its convergence (basic idea). Convergence of infinite series. Comparison test, ratio test root, test. Raabe’s test, Logarithmic ratio test, Cauchy’s condensation test, De Morgan and Bertrand test and higher logarithmic ratio test. Alternating series, Leibnitz test, Absolute and conditional convergence. Congruence modulo m-relation, Equivalence relations and partitions.
| Sr | Chapter Name | No Of Page |
|---|---|---|
| 1 | PAPER–I : ALGEBRA AND TRIGONOMETRY,SEQUENCE | 11 |
| 2 | INFINITE SERIES | 13 |
| 3 | GROUPS AND SIMPLE PROPERTIES | 19 |
| 4 | SUB-GROUP | 5 |
| 5 | COSETS AND COSETS DECOMPOSITION | 18 |
| 6 | PERMUTATION GROUP TRANSFORMATION GROUP AND CAYLEY’S THEOREM | 8 |
| 7 | RING, FIELD INTEGRAL DOMAIN | 8 |
| 8 | TRANSCENDENTAL FUNCTIONS OF COMPLEX QUANTITIES | 62 |
| 9 | PAPER–II : CALCULUS,Î-d DEFINITION OF THE LIMIT OF A FUNCTION | 9 |
| 10 | CONTINUOUS FUNCTIONS AND CLASSIFICATION OF DISCONTINUTIES | 8 |
| 11 | DIFFERENTIABILITY | 6 |
| 12 | ROLLE’S THEOREM, FIRST AND SECOND MEAN VALUE THEOREM, TAYLOR’S THEOREM WITH LAGRANGE’S AND CAUCHY’S FORMS OF REMAINDER | 7 |
| 13 | SUCCESSIVE DIFFERENTIATION AND LEIBNITZ’S THEOREM | 10 |
| 14 | EXPANSION OF FUNCTIONS | 6 |
| 15 | INDETERMINATE FORMS | 8 |
| 16 | PARTIAL DIFFERENTIATIONS | 9 |
| 17 | JACOBIANS | 9 |
| 18 | MAXIMA AND MINIMA | 11 |
| 19 | TANGENTS AND NORMAL | 13 |
| 20 | CURVATURE | 13 |
| 21 | ENVELOPS, EVOLUTES AND INVOLUTES | 8 |
| 22 | ASYMPTOTES | 8 |
| 23 | SINGULAR POINTS : CURVE TRACING | 8 |
| 24 | REDUCTION FORMULA | 11 |
| 25 | BETA AND GAMMA FUNCTION | 8 |
| 26 | LENGTH OF CURVES (RECTIFICATION) | 6 |
| 27 | QUADRATURE | 6 |
| 28 | SURFACE AND VOLUME OF SOLIDS OF REVOLUTION | 7 |
| 29 | MULTIPLE INTEGRALS | 45 |
| 30 | PAPER–III : GEOMETRY AND VECTOR CALCULUS,CONFOCAL CONICS | 5 |
| 31 | POLAR EQUATION OF A CONIC | 18 |
| 32 | CARTESIAN CO-CORDINATES SYSTEM | 18 |
| 33 | THE PLANE | 16 |
| 34 | THE STRAIGHT LINE | 18 |
| 35 | THE SPHERE | 19 |
| 36 | THE CONE AND CYLINDER | 22 |
| 37 | CONICOIDS | 20 |
| 38 | DERIVATIVE OF VECTOR IS TERMS OF ITS COMPONENTS | 20 |
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