Differential Equations (S. L. Ross)
Differential Equations with Applications and Historical Notes (George F. Simmons)
First order ordinary differential equations
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.)
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
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
Series solutions (power series, Frobenius method)
Legendre and Bessel functions and their orthogonal properties
Systems of linear first order ordinary differential equations