Bessel Equation: Introduction

This lecture introduces the Bessel equation, which is crucial in solving physical problems like wave equations in circular systems. It covers the systematic procedure for solving scalar linear 2nd order ODEs, including the Frobenius method and variation of parameters. The Fuchs Theorem and its application around regular singular points are discussed, along with the significance of Bessel functions in eigenvalue problems. Examples of eigenmodes of vibration in circular systems are presented, illustrating the practical application of the series substitution method.