Airy functions have been long important in various areas of mathematics, physics, and astronomy. Even though the Airy differential equation looks extremely simple, its solutions are generally ‘notorious’ in nature. In this expository article, we have given a thorough description of the Airy functions with real arguments. Majority of the books (with the exception of specialized books on the subject) do not pay attention in detail to these functions. Taking this as a motivating factor, we have written this article for postgraduates and students be-ginning research to help them understand the nitty-gritty of these beautiful functions. The solutions of the Airy differential equation called the Airy and Bairy functions are explained in detail. Finally, we have given some ideas to numerically ob-tain these functions.

Reckoning the importance of Airy functions and their overwhelming applications, we present here the derivation of their asymptotic forms for real arguments in detail as a continuation to the part I of the article. When needed, the associated concepts and the insights are motivated so that the reader is not left in the dark. Finally, some physical situations where this differential equation appears are explained.