This course on differential equations aims to teach students the concepts and methods related to first and second-order differential equations, including reducible forms, exact equations, and higher-order linear equations. The course covers various solution methods such as Laplace transform, Picard method, and numerical techniques like Runge Kutta and Milne predictor-corrector methods. The intended audience for this course includes learners interested in advanced mathematics and those seeking to deepen their understanding of differential equations and their applications.
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
