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4]P.M.C. Part-I (Semester-I) Syllabus a, theorem, Darboux’s intermediate value theorem for derivatives, Chain, rule, indeterminate forms., , Unit III : Rolle's theorem, Lagrange and Cauchy Mean value theorem,, mean value theorems of higher order, Taylor’s theorem with various, forms of remainders, Succession differentiation, Leibnitz theorem,, Maclaurin and Taylor’s series, Partial differentiation, Euler’s theorem on, homogeneous function., , Unit IV : Tangent and normal, Asymptomatic Curvature, Envelops and, evolutest, Tests for concavity and convexity, Points of inflexion, Mul, tiple points, Parametric representation, Tracing of curves in Cartesian, and Polar forms., , Part-B, Integral Calculus, , Unit V : Definite integrals as limit of the sum, Riemann integral, Integrabil, ity of continuous and monotonic functions, Fundamental theorem of, integral calculus, Mean value theorems of integral calculus, Differentia, tion under the sign of Integration., , Unit VI : Improper integrals, their classification and convergence, Com, parison test, p-test, Abel's test, Dirichlet's test, quotient test, Beta and, Gamma functions. :, , Unit VII : Rectification, Volumes and Surfaces of Solid of revolution. Pap, pus theorem. Multiple integrals, change of order of double integration,, Dirichlet’s theorem, Liouville’s theorem for multiple integrals., , Unit VIII : Sector Differentiation, Gradient, Divergence and Curl, Normal, on a surface, Directional Derivative, Vector Integration, Theorems of, iauss, Green, Stokes and related problems.