Ordinary Differential Equations
The complete syllabus for Ordinary Differential Equations, the second Minor mathematics paper for B.Sc / B.A. First Year at Madhya Pradesh state universities under NEP 2020 — a 4-credit, 60-hour course. Four modules cover the Indian Knowledge System, linear and exact equations, first-order higher-degree equations, linear equations with constant coefficients, and the method of variation of parameters with simultaneous equations. Available in English and Hindi editions.
Ordinary Differential Equations · English
by Dr. H.K. Pathak · ₹275 — covers this full syllabus.
Sadharan Avkal Sameekaran (साधरण अवकल समीकरण) · Hindi
by Dr. H.K. Pathak · ₹275 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Indian Knowledge System
Historical background of differential equations and the contributions of Indian mathematicians — Aryabhata, Bhaskaracharya and Madhava.
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.
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 · Industrial Applications (Case Study)
Applications of differential equations to problems in industry, business and economics.