Calculus and Vector Analysis | B.A./B.Sc. First Year Major-2 | NEP 2020 Syllabus of All Madhya Pradesh Universities | Vedic Calculus, Solved Papers, MCQs & HOTS | Dr. H.K. Pathak

Open your Major-2 syllabus and look at Unit-I. It does not ask for general calculus. It names Aryabhata, Madhava and Jyeshthadeva, and then it names the sutras: differentiation using Dhvaja Ghata Sutra, successive differentiation using Urdhva-Triyagbhyam Sutra, integration using Ekadhikena Purvena and Paravartya Yoja Sutra, and the Vedic approach to areas under curves. That is ten lectures of your paper, and no national calculus textbook contains a word of it. This book was written for the MP syllabus, so it opens where your paper opens.

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 tracing of curves in Cartesian and polar form; integral calculus through double and triple integrals, reduction formulae, quadrature, rectification and volumes of revolution; vector differentiation, gradient, divergence, curl and vector identities; and vector integration with Gauss, Green and Stoke theorems, curves in space, curvature and torsion, and the Frenet-Seret formulae.

It also carries the Case Study module on Industrial Applications - calculus applied to business and economics, vector calculus to real-world problems - a marked component general textbooks have no reason to include.

652 pages in one volume, where other publishers split this paper across two titles.

Every chapter carries solved examples building to exam standard, followed by MCQs, Objective Questions and HOTS problems, with previous year papers solved in full.

Written by Dr. H.K. Pathak, Ex-Professor and Head, School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, former Dean of Science, cited over 3,300 times. Read by students at Vikram Ujjain, DAVV Indore, Jiwaji Gwalior, RDVV Jabalpur, Barkatullah Bhopal, Dr. Harisingh Gour Sagar and APS Rewa.

Also available in Hindi as Kalan aur Sadish Vishleshan.