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
The content would be covered soon.
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