Differential Equations
The complete B.Sc syllabus for Differential Equations (MASC-03), the third-semester core mathematics course of the Bachelor of Science programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — first-order and higher-degree differential equations, linear and simultaneous ODEs, and first- and higher-order partial differential equations. Available in English and Hindi editions.
Differential Equations · English
by Dr. H.K. Pathak · ₹470 — covers this full syllabus.
Avkal Sameekaran (अवकल समीकरण) · Hindi
by Dr. H.K. Pathak · ₹470 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · First Order & Higher Degree Differential Equations
Contributions of Indian mathematicians (Aryabhatta, Varahmihir, Bhaskar-I, Shreedharacharya, Shreepati, Parmeshwar). Differential equations of first order and first degree — variables separable, homogeneous, linear and equations reducible to linear form, exact equations and integrating factor; first-order higher-degree equations solvable for x, y and p, Clairaut's form and singular solutions, orthogonal trajectories.
Unit 2 · Linear & Simultaneous Ordinary Differential Equations
Linear differential equations with constant coefficients, homogeneous linear ODEs, linear differential equations of second order, transformation of the equation by changing the dependent or independent variable, method of variation of parameters, and ordinary simultaneous differential equations.
Unit 3 · First Order Partial Differential Equations
Lagrange's solution; some special types of equations solvable by methods other than the general method; Charpit's general method of solution.
Unit 4 · Second & Higher Order Partial Differential Equations
Classification of linear PDEs of second order, homogeneous and non-homogeneous equations with constant coefficients, PDEs reducible to equations with constant coefficients, and Monge's method.