Mathematics (M.Sc. ENTRANCE EXAMINATIONS)

CONTENTSPreface —Pgs. vJoint Admission Test for M Sc (JAM) —Pgs. viiMODULE I1. Sequences and Series of Real Numbers —Pgs. 31.1 Sequence and Series —Pgs. 31.2 Bounds of A Sequence —Pgs. 71.3 Oscillatory Sequence —Pgs. 91.4 Algebra of Sequence —Pgs. 131.5 Cauchy Sequence —Pgs. 141.6 Infinite Series —Pgs. 161.7 Tests for Series —Pgs. 19Mock Test Module I —Pgs. 37MODULE II2. Functions of One, Two or Three Real Variables I —Pgs.492.1 Differentiation —Pgs. 492.2 Mean Value Theorem —Pgs. 512.3 Indeterminate Forms —Pgs. 563. Functions of One, Two or Three Real Variables II —Pgs. 873.1 Differential Coefficients —Pgs. 873.2 Rules for Differentiation —Pgs. 874. Functions of One, Two or Three Real Variables III —Pgs.1134.1 Applications of Derivatives —Pgs. 1134.2 Maximum and Minimum —Pgs. 1134.3 Monotonic Function —Pgs. 1144.4 Rolle's and Lagrange's Theorem —Pgs. 115Mock Test Module II —Pgs. 151MODULE III5. Integration I —Pgs. 1675.1 Indefinite Integration —Pgs. 1675.2 Rules and Methods of Integration —Pgs. 1675.3 Integration of Rational Fractions —Pgs. 1695.4 Integration of Irrational Fractions —Pgs. 1706. Integration II —Pgs. 2016.1 Definite Integration —Pgs. 2016.2 Definite Integration and Areas —Pgs. 2026.3 Sketches of Curves —Pgs. 2036.4 Line Integral —Pgs. 2046.5 Double Integrals —Pgs. 2056.6 Triple Integrals —Pgs. 2086.7 Stoke's and Gauss Divergence Theorem —Pgs. 210Mock Test Module III —Pgs. 241MODULE IV7. Differential Equations —Pgs. 2577.1 Differential Equations —Pgs. 2577.2 Formation of Differential Equation —Pgs. 2587.3 Solution of Differential Equation —Pgs. 2587.4 Tangent and Normal —Pgs. 2597.5 Equation Reducible To A Linear Form —Pgs. 2597.6 Applications of Differential Equations —Pgs. 2657.7 Trajectories —Pgs. 2667.8 Particular Integral —Pgs. 2697.9 Homogeneous Linear Equation —Pgs. 271Mock Test Module IV —Pgs. 303MODULE V8. Vector Algebra —Pgs. 3198.1 Vectors and Their Representation —Pgs. 3198.2 Straight Lines —Pgs. 3208.3 Plane —Pgs. 3218.4 Product of Vectors —Pgs. 3219. Vector Calculus —Pgs. 3539.1 Differential Operators —Pgs. 3539.2 Vector Identities —Pgs. 3589.3 Gauss's, Stoke's and Green's Theorems —Pgs. 360Mock Test Module V —Pgs. 391MODULE VI10. Group Theory —Pgs. 40310.1 Integer —Pgs. 40310.2 Group Theory —Pgs. 40310.3 Subgroup —Pgs. 40710.4 Homomorphism —Pgs. 41410.5 Isomorphism —Pgs. 41410.6 Automorphism —Pgs. 41611. Linear Algebra —Pgs. 43911.1 Vector Space —Pgs. 43911.2 Vector Subspaces —Pgs. 44011.3 Algebra of Subspaces —Pgs. 44111.4 Isomorphism —Pgs. 44211.5 Linear Functional —Pgs. 44411.6 Linear Transformations —Pgs. 44511.7 Matrices —Pgs. 45011.8 Invariance and Reducibility —Pgs. 45511.9 Matrix of A Projection —Pgs. 45712. Real Analysis —Pgs. 48112.1 Power Series —Pgs. 48112.2 Differentiation and Integration of Ps —Pgs. 481Mock Test Module VI —Pgs. 489MOCK TEST MATHEMATICS —Pgs. 503