This course covers the Series Solution of Differential Equations, including Ordinary and Singular Points, Legendre Polynomials, Frobenius Method, Bessel's Equation, and Clairaut's Equation. Students will learn to solve differential equations of various degrees and orders, as well as simultaneous linear differential equations. The course teaches skills such as finding recurrence relations, proofs, and important example problems related to Bessel's Functions and Legendre Polynomials. The teaching method includes theoretical explanations, proofs, and example problems. This course is intended for students and professionals interested in advanced topics in differential equations and mathematical methods in physics.
Overview
Syllabus
Series Solution of Differential Equation | Ordinary Point and Singular Point.
Series Solution of Differential Equation | Legendre Polynomial | Power Series Method.
Series Solution of Differential Equation | Frobenius Method | Power Series Method.
Series Solution of Differential Equation | Frobenius Method | Bessel's equation.
Differential Equation | Solvable For p | First Order & Higher Degree.
Differential Equation | Solvable For y | First Order & Higher Degree.
Differential Equation | Solvable For x | First Order & Higher Degree.
Differential Equation | Clairaut's Equation | First Order & Higher Degree.
Differential Equation | Simultaneous Linear Differential Equation.
Differential Equation | Simultaneous Linear Differential Equation |P-2.
Bessel's Function | Recurrence Relation of Bessel's Function | Proofs.
Bessel's Function | Recurrence Relation of Bessel's Function | Part-II.
Bessel's Function | Important Example Problem of Bessel's Function.
Bessel's Function | Orthogonal Property of Bessel Function | Proof.
Legendre Polynomial | Rodrigues Formula | Proof of Rodrigues Formula.
Legendre Polynomials | Generating Function of Legendre Polynomial.
Legendre Polynomials | Recurrence Relation Of Legendre Polynomials.
Legendre Polynomial | Orthogonal Properties of Legendre Polynomial.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part -I.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-II.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-III.
Partial Differential Equation | Homogeneous PDE | CF & PI | Part-IV.
Partial Differential Equation | General Method To Find PI | Part-V.
Partial Differential Equation | Non Homogeneous PDE | Rules of CF & PI.
Coronavirus | How To Protect Your Self | Advice For Students & Community Members.
Taught by
Gajendra Purohit
