#2 Preliminaries Regarding the Differential Equations
Differential Equations;

w.r.t. number of independent variables

w.r.t. dependent variables

w.r.t. the presence of a Source Term
SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
The general form of an Ordinary Differential Equation (ODE) of order 2 may be taken as
Which may be linear or nonlinear, homogeneous or nonhomogeneous.
#3 Introduction to SturmLiouville System
There are many second order, ordinary, Homogeneous, Linear Differential equations which appear in physical and Engineering problems: Some of these are
All these Differential Equations are special cases of more general type of second order, ordinary, homogeneous, Linear Differential Equation are known as SturmLiouville’s Equations and the Differential Equation together with appropriate (Suitable) boundary conditions is known as SturmLiouville system (Problem).
Note: John Sturm and Joseph Liouvi are French Mathematics who did work on such Differential Equations on 1830
#4 SturmLiouville Equation (S.L Equation)
The second order, ordinary, homogeneous, linear differential equation of the form
Notation: In term of Linear Differential operator: If we define the operator L as
#5 What is the SelfAdjoint SturmLiouville differential operator notation?
#6 Properties of SturmLiouville Equations
#9 Regular & Periodic Sturm Liouville System
Regular Sturm Liouville [S.L.] System
The Regular S.L. Equation together with linear, homogeneous, separated (.e., no mixing of) end point (boundary) conditions
Note: The system is regular when zero is not the point of the given interval.
Periodic Sturm Liouville [S.L.] System
The periodic S.L. Equation together with linear, homogeneous mixed and periodic end point conditions