Differential Equation and Geometry

About this book

Differential Equation and Geometry by Dr. H.K. Pathak covers the Madhya Pradesh Major-3 paper in one volume, written unit for unit against the NEP 2020 syllabus.

Unit-I is the most unusual unit across all three Major papers: the historical background of differential equations and the contributions of Aryabhata, Bhaskaracharya and Madhava; ancient geometry and the Shulb Sutra; the contributions of Baudhayana, Katyayana, Nilkanth Somayaji, Parameshwaran and Shankar Variyar; and the triplets of Vedic Geometry — addition and subtraction of triplets, and triplets for double and half angles. There is no national textbook and no reliable source for this material, and it is ten full lectures of your paper.

From there the book follows the syllabus in order through linear and exact differential equations, first order higher degree equations, Clairaut's equation, singular solutions and orthogonal trajectories; linear equations with constant coefficients and second order linear equations; variation of parameters and simultaneous equations of first order; the general equation of the second degree, conics and polar equations; and Cone and Cylinder — generators, the condition for three mutually perpendicular generators, right circular cone, right circular cylinder and enveloping cylinder, which alone carries 20 lectures. The Case Study module on Industrial Applications is included. Also available in Hindi. Published by Shree Shiksha Sahitya Prakashan, Meerut.