Explore a comprehensive 23-hour video playlist on differential equations covering first-order and higher-order equations, linear and nonlinear systems, and various solution methods. Learn about exact and reducible equations, Cauchy-Euler equations, Laplace transforms, and numerical methods like Picard, Euler modified, and Runge-Kutta. Delve into series solutions, Bessel functions, Legendre polynomials, and partial differential equations. Master topics such as Wronskian, orthogonal trajectories, and singular solutions. Gain practical problem-solving skills through numerous examples and applications in this in-depth tutorial series by Dr. Gajendra Purohit.
Overview
Syllabus
Differential Equation First Order and Degree |Methods & Solution.
Differential Equation Reducible to Linear form | Lecture-II by GP Sir.
Exact and Reducible to Exact differential equation of first order.
Linear Higher Order Differential Equation | CF & PI |Lecture-I.
Linear Higher Order Differential Equations, Rules of CF & PI By GP Sir.
Homogeneous cauchy-euler Second Order Differential Equations By GP Sir.
Second Order Exact Differential Equation with Variable Coefficient.
Solution of Second Order Differential Equation | Part of CF is Known.
Second Order Differential Equation - Change of Dependent Variable Method.
Second Order Differential Equation - Change of Independent Variable Method.
Variation of Parameter Method - Second Order Differential Equation | Gp.
Laplace Transform | Application to Ordinary Differential Equation | GP.
Picard method of successive approximations Example for solving ODE.
Euler Modified Method - Solution Of ODE By Numerical Method | Example.
Runge Kutta Method of 4th Order - Solution of ODE By Numerical Method.
Milne Predictor & Corrector Method - Solution Of ODE Numerical Method.
Adam Bashforth Predictor And Corrector Method - Solution Of ODE By NA.
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.
Partial Differential Equation | Non Homogeneous PDE | Rules of PI.
Ordinary Differential Equation , CSIR- NET (Maths) , Previous Paper Solution,.
CSIR NET, What Is CSIR NET EXAM, Important Topics & Tips By GP Sir.
Successive Differentiation | Differential Calculus | Concepts & Examples.
Successive Differentiation | nth Derivative | Differential Calculus.
Leibnitz Theorem | Successive Differentiation | nth Derivative | Part-I.
Leibnitz Theorem | Successive Differentiation | nth Derivative | Part-II.
Leibnitz Theorem | nth Differential Coefficient For Special Value of x | Part-III.
Maclaurin Series | Maclaurin Theorem | Proof & Series Expansion | Part-I.
Maclaurin Series | Maclaurin Theorem | Example & Solutions | Part-II.
Taylor Series | Taylor Theorem | Proof & Series Expansion | Part-I.
Taylor Series | Taylor Theorem | Example & Solutions | Part-II.
Differentiability | Two Variable Function | Multivariable Calculus.
Coronavirus | How To Protect Your Self | Advice For Students & Community Members.
Differential Equation - Wronskian | linearly independent & Dependent Solution | Abel's Formula.
Variation of Parameter Method - Wronskian | Differential Equation.
Orthogonal Trajectories - Differential Equation | Definition & Examples.
Orthogonal Trajectories - Polar Form | Differential Equation.
Singular Solution - Differential Equation | Singular Solution Examples.
Differential Equation | Order And Degree With Concept & Example By GP Sir.
Differential Equation | Formation Of Differential Equation - Concept & Example By GP Sir.
Differential Equation | Variable Separable Method - Concept & Example By GP Sir.
Differential Equation | Reducible Into Separation Of Variable - Concept & Example By GP Sir.
Differential Equation | HOMOGENEOUS Differential Equation - Concept & Example By GP Sir.
Differential Equation | REDUCIBLE HOMOGENEOUS Differential Equation - Concept & Example By GP Sir.
Differential Equation | Linear Differential Equation - Concept & Example By GP Sir.
Differential Equation | Reducible Linear Differential Equation - Concept & Example By GP Sir.
Differential Equation | Exact Differential Equation - Concept & Example By GP Sir.
Differential Equation | Reducible Exact Differential Equation PART 1 - Concept & Example By GP Sir.
Differential Equation | Reducible Exact Differential Equation PART 2 - Concept & Example By GP Sir.
Differential Equation | Reducible Exact Differential Equation PART 3 - Concept & Example By GP Sir.
Differential Equation | First Order And Higher Degree (Solvable For P) | By GP Sir.
Differential Equation | First Order And Higher Degree (Solvable For X) | By GP Sir.
Differential Equation | First Order And Higher Degree (Solvable For Y) | By GP Sir.
Differential Equation | Clairaut's Equation | First Order & Higher Degree | By GP Sir.
Differential Equation | Higher Order Differential Equations - Complementary Function | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral Part 2 | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral Part 3 | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral Part 4 | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral Part 5 | By GP Sir.
Differential Equation | Higher Order Differential Equations - Particular Integral Part 6 | By GP Sir.
Differential Equation | Reducible Into Differential Equation With Constant Coefficient | By GP Sir.
Differential Equation | Reducible Into Differential Equation With Constant Coefficient Part 2 GP Sir.
Taught by
Gajendra Purohit
