#2 Preliminaries Regarding the 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 non-linear, homogeneous or non-homogeneous.
#3 Introduction to Sturm-Liouville 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 Sturm-Liouville’s Equations and the Differential Equation together with appropriate (Suitable) boundary conditions is known as Sturm-Liouville system (Problem).
Note: John Sturm and Joseph Liouvi are French Mathematics who did work on such Differential Equations on 1830
#4 Sturm-Liouville 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 Self-Adjoint Sturm-Liouville differential operator notation?
#6 Properties of Sturm-Liouville 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
#23 Wronskian of Two Functions