Calculus and Vector Analysis

About this book

Competitors split this paper across two books, a calculus title and a vector title, and topics fall through the join while students buy twice. This is the whole Major-2 paper in one 652-page volume.

Unit-I is Vedic Calculus, and it is sharper than the Algebra book's Indian Knowledge System unit because the syllabus names specific sutras: differentiation by Dhvaja Ghata Sutra, successive differentiation and division of polynomials by Urdhva-Triyagbhyam Sutra, integration by Ekadhikena Purvena and Paravartya Yoja Sutra, and the Vedic approach to areas under curves. Ten lectures a student cannot improvise from a general textbook or from the internet.

From there it follows your modules in order: successive differentiation with Leibnitz, Maclaurin and Taylor; partial derivatives and asymptotes; curvature, concavity, points of inflexion, singular and multiple points and curve tracing; integral calculus through double and triple integrals, reduction formulae, quadrature, rectification and volumes of revolution; vector differentiation with gradient, divergence, curl and vector identities; and vector integration with the Gauss, Green and Stokes theorems, curves in space, curvature and torsion and the Frenet-Serret formulae. The Case Study module on Industrial Applications is included. Published by Shree Shiksha Sahitya Prakashan, Meerut.