A Compendium of Computational Methods for Calculus

The evolution of calculus has greatly changed science and engineering as we know it. As Newton and Leibniz put it to inception back in the 17th century, it serves as the backbone for modern engineering and science. It helps us analyze change and accumulation in a given context. But what about the real-world problems that are far more complex than analyzing functions? This is where derivatives, integrals, and differential equations come into discussion, and the need to approximate solutions arise. Ranging from basic mathematical techniques to advanced machine learning, computational methods have greatly transformed. The approach towards these methods is far more simplistic than traditional techniques, and thus has served fields like physics, economics, artificial intelligence, and more. This paper attempts to highlight these new techniques and the dramatic impact that methodology shifts serve. Alongside collating the history of these new approaches and their use in solving far more complex problems, it highlights the shifts and ease in tackling problems from various domains. Understanding the significance of modern computation serves advanced knowledge in science and fosters innovation (Almeida et al., 2020).