DIFFERENTIAL EQUATION NOTES IN PDF | DIFFERENTIAL EQUATION NOTES IN PDF-CSIR NET / GATE MATHS / IIT JAM MATHS

 In this article i have discussed notes of DIFFERENTIAL EQUATION is which is also helpful to Engineering students , B.Sc. and M.Sc. students.

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DIFFERENTIAL EQUATION is most important topic form competitive examination for science students. Every examination asked more question related to DIFFERENTIAL EQUATION

in this article i will provided following type notes related to DIFFERENTIAL EQUATION

DIFFERENTIAL EQUATION   PDF NOTES  |  

DIFFERENTIAL EQUATION NOTES IN PDF-CSIR NET / GATE MATHS / IIT JAM MATHS 

CSIR NET -

 DIFFERENTIAL EQUATION SYLLABUS 

Existence and uniqueness of solutions of initial value problems for first order ordinary differential equations, 

singular solutions of first order ODEs, 

system of first order ODEs.

 General theory of homogenous and non-homogeneous linear ODEs, 

variation of parameters, 

 Sturm-Liouville boundary value problem, Green’s function

Calculus of Variations: Variation of a functional, Euler-Lagrange equation, Necessary and sufficient conditions for extrema. Variational methods for boundary value problems in ordinary and partial differential equations. Linear Integral Equations: Linear integral equation of the first and second kind of Fredholm and Volterra type, Solutions with separable kernels. Characteristic numbers and eigenfunctions, resolvent kernel

GATE MATHS - 

DIFFERENTIAL EQUATION SYLLABUS 

• First order ordinary differential equations, 
• existence and uniqueness theorems for initial value problems, 
• linear ordinary differential equations of higher order with constant coefficients; Second order linear ordinary differential equations with variable coefficients; 
• Cauchy-Euler equation, method of Laplace transforms for solving ordinary differential equations,
•  series solutions (power series, Frobenius method);
• Legendre and Bessel functions and their orthogonal properties; 
• Systems of linear first order ordinary differential equations, 
• Sturm’s oscillation and separation theorems, 
• Sturm-Liouville eigenvalue problems, 
• Planar autonomous systems of ordinary differential equations: Stability of stationary points for linear systems with constant coefficients, Linearized stability, Lyapunov functions.

IIT JAM-

DIFFERENTIAL EQUATION SYLLABUS 

.Ordinary differential equations of the first order of the form y'=f(x,y), 

.Bernoulli’s equation, exact differential equations, integrating factor, 

.orthogonal trajectories, homogeneous differential equations, 

.variable separable equations, linear differential equations of second order with constant coefficients,

. method of variation of parameters, 

.Cauchy-Euler equation.

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