ODE Special Purpose Packs

Pack-1

After a brief discussion of some selected properties, Forbenius method of series solution is explained with help of four examples of second order ordinary linear differential equations. The four examples correspond to four different cases that arise depending on the nature of roots of the indicial equation.
Reference: H.T.H Piaggio, "Ordinary Differential Equations"                                                                 

 Lectures given at IIT Bhubaneswar as Part of Mathematical Physics Course 2016
 Download Link at the end of the page (File Name 16MP-ODE-IITBBS.pdf)

Pack-2

The Frobenius method classifies the series solutions into four cases depending on the nature of roots of the indicial equation. The Bessel's equation for different parameter  values gives rise the four cases. One solution is easy to obtain as is the case for any ODE  solvable by the Frobenious method. The second second solution leads to introdcution  of  Bessel functions of second kind. 

Lectures given at IIT Bhubaneswar as Part of Mathematical Physics Course 2017 (WORKING ON IT)