Basic Calculus and Vector Calculus

Unit 1 · Indian Knowledge System & Vedic Calculus

Contributions of Indian mathematicians to calculus — Aryabhata, Madhava and Jyeshthadeva. Vedic calculus — differentiation by the Dhvaja-Ghata sutra, successive differentiation and derivative of a quotient of polynomials by the Urdhva-Triyagbhyam sutra, integration by the Ekadhikena Purvena and Paravartya Yojayet sutras, integration of a product of functions, and the Vedic approach to areas under curves.

Unit 2 · Differential Calculus

Successive differentiation, Leibnitz theorem, Maclaurin's and Taylor's series; partial derivatives of functions of two and three variables; asymptotes of algebraic and polar curves; curvature — radius of curvature, curvature at the origin and centre of curvature.

Unit 3 · Integral Calculus

Integration of transcendental functions; reduction formulae; the definite integral; double and triple integrals.

Unit 4 · Vector Calculus

Vector differentiation and rules of differentiation, derivatives of triple products; gradient, divergence and curl; directional derivatives; vector identities; vector integration.

Unit 5 · Industrial Applications (Case Study)

Applications of calculus and vector calculus to problems in industry, business and the real world.