Krishna's - Calculus

SYLLABUS- CALCULUS,
Differential Calculus
Unit-1: e-definition of the limit of a function, Continuous functions and classification of discontinuities, Differentiability, Chain rule of Differentiability, Rolle's theorem, First and second mean value theorems, Taylor's theorems with Lagrange's and Cauchy's forms of remainder, Successive differentiation and Leibnitz's theorem.
Unit-2: Expansion of functions (in Taylor's and Maclaurin's series), Indeterminate forms, Partial differentiation and Euler's theorem, Jacobians.
Unit-3: Maxima and Minima (for functions of two variables), Tangents and normals (polar form only), Curvature, Envelopes and evolutes.
Unit-4(a): Asymptotes, Tests for concavity and convexity, Points of inflexion, Multiple points, Tracing of curves in Cartesian and Polar coordinates.
Integral Calculus
Unit- 4(b): Reduction formulae, Beta and Gamma functions.
Unit-5: Quadrature. Rectification. Volumes and surfaces of solids of revolution, Pappus theorem, Double and triple integrals, Change of order of integration, Dirichlet's and Liouville's integral formulae.