Ordinary Differential Equations

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Syllabus for Ordinary Differential equations

Formulation of differential equations

Equations of first order and first degree

Integrating factor

Orthogonal trajectory

Equations of first order but not of first degree

Clairaut’s equation

Singular solution

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)


Second and higher order linear equations with constant coefficients


Complementary function


Particular integral and general solution


Second order linear equations with variable coefficients


Euler-Cauchy equation


Determination of complete solution when one solution is known using method of variation of parameters


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Laplace and Inverse Laplace transforms and their properties


Laplace transforms of elementary functions


Application to initial value problems for 2nd order linear equations with constant coefficients


Lecture 1: Laplace transformation


Lecture 2: Laplace transformation


Lecture 3: Laplace transformation


Lecture 4: Laplace transformation


Lecture 5: Laplace transformation


Lecture 6: Laplace transformation


Lecture 7: Laplace transformation


Lecture 8: Laplace transformation


Lecture 9: Laplace transformation


Lecture 10: Laplace transformation


Lecture 11: Laplace transformation


Lecture 12: Laplace transformation