Dive into a comprehensive 7-hour video series on advanced differential equations and mathematical functions. Explore series solutions for ordinary and singular points, Legendre polynomials, and the Frobenius method. Master techniques for solving first-order and higher-degree differential equations, including Clairaut's equation and simultaneous linear differential equations. Delve into Bessel's functions, studying their recurrence relations, orthogonal properties, and practical applications. Examine Legendre polynomials, covering Rodrigues formula, generating functions, and orthogonal properties. Tackle partial differential equations, focusing on homogeneous and non-homogeneous cases, complementary functions, and particular integrals. Conclude with essential advice on protecting yourself during the coronavirus pandemic.
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
