Differential Equations and Geometry
The complete syllabus for Differential Equations and Geometry, the third Major (core) mathematics paper for B.Sc / B.A. First Year at Madhya Pradesh state universities under NEP 2020 — a 6-credit, 90-hour course. Six modules span the Indian Knowledge System and Vedic geometry, ordinary differential equations (linear, exact and higher-degree, variation of parameters and simultaneous equations), the geometry of conics, and the cone and cylinder in three dimensions. Available in English and Hindi editions.
Differential Equation and Geometry · English
by Dr. H.K. Pathak · ₹450 — covers this full syllabus.
Avkal Sameekaran aur Jyamiti (अवकल समीकरण और ज्यामिति) · Hindi
by Dr. H.K. Pathak · ₹410 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Indian Knowledge System & Vedic Geometry
Historical background of differential equations and the contributions of Aryabhata, Bhaskaracharya and Madhava; ancient geometry and the Shulba Sutra, with the contributions of Baudhayana, Katyayana, Nilkanth Somayaji, Parameshwaran and Shankara Variyar; Vedic geometry — triplets, their addition and subtraction, and triplets for double and half angles.
Unit 2 · Differential Equations – I
Linear differential equations and equations reducible to linear form, change of variables; exact differential equations; first-order higher-degree equations solvable for x, y and p, equations homogeneous in x and y, Clairaut's equation and singular solutions; geometrical meaning of a differential equation and orthogonal trajectories.
Unit 3 · Differential Equations – II
Linear differential equations with constant coefficients; homogeneous linear ordinary differential equations; linear differential equations of the second order.
Unit 4 · Differential Equations – III
Method of variation of parameters; ordinary simultaneous differential equations of the first order.
Unit 5 · Geometry – I: Conics
General equation of the second degree; tracing of conics; system of conics; polar equation of a conic.
Unit 6 · Geometry – II: Cone & Cylinder
Cone — equation of a cone with a given base, generators, condition for three mutually perpendicular generators, right circular cone; cylinder — equation and properties, right circular cylinder, enveloping cylinder.
Unit 7 · Industrial Applications (Case Study)
Applications of differential equations and geometry to problems in industry, business and the real world.