Musical instruments that start with the letter I include the igil, ipu, Irish uillean, Irish bouzouki, ichigenkin, inci, iya, itotele and istarski mih. The instruments originate from countries ranging from Cuba and Ireland to Croatia, Japan and the Philippines.
Bessel's functions are often used in acoustics for describing circular membranes behaviour (exploited by most of the musical instruments). They are the solutions of the wave equations using polar coordinates. Set the properties of the membrane Bessel's functions describe the vibrational modes of the membrane.
One of the most important applications of differential calculus is to find extreme function values. The calculus methods for finding the maximum and minimum values of a function are the basic tools of optimization theory, a very active branch of mathematical research applied to nearly all fields of practical endeavor.