ordinary differential equations (ode)

Good Books for reference:

  1. Differential Equations (S. L. Ross)

  2. Differential Equations with Applications and Historical Notes (George F. Simmons)


Syllabus for ordinary differential equations (ODEs)

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


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General theory of homogenous and non-homogeneous linear ODEs


Lecture 1: ODE (what is an ODE?)


Lecture 2: ODE (A basic model involving an ODE: An object falling in atmosphere)


Lecture 3: ODE (A basic model involving an ODE: mice and cats in a field)


Lecture 4: ODE (Direction Field of a first order ODE)


Lecture 5: ODE (Observations from Direction Fields)


Lecture 6: ODE (Why classification of differential equations is required?)


Lecture 7: ODE (Classification of differential equations)


Lecture 8: ODE (Explicit solutions of differential equations)


Lecture 9: ODE (Implicit solutions of ODEs)


Lecture 10: ODE (General, particular and singular solutions of ODEs)


Lecture 11: ODE (Classification of solutions of differential equations is undesirable.)


Lecture 12: ODE (Variable separable differential equations)


Lecture 13: ODE (Equations reducible to variable separable form.)


Lecture 14: ODE (Homogeneous differential equations)


Variation of parameters


Sturm-Liouville boundary value problem


Green’s function


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