Journal of Applied & Computational Mathematics

This article outlines Isaac Newton's most significant contributions to mathematics and physics and their computer implementation. The following two software tools were used to describe the results: Wolfram Mathematica and StereoMV (Java3D-based author's software). Isaac Newton laid the foundations of differential and integral calculus. Through the principles of the method of fluxes, he expresses the reciprocal nature of the operations of integration and differentiation. He is writing the integrals and derivatives in two columns. With the help of Wolfram Mathematica software, it is easy to confirm Newton's discovery by drawing graphs. At the same time, with this discovery, the scientist laid the foundations of numerical methods, which, as is known today, can be used with the help of the computer. Newton was the first to introduce the concept of limit, which is known to be used in mathematical analysis. He presents it by the method of limits in 12 lemmas. In this paper, a new approach based on the method is given, with the help of which the computer can draw a regular polygon, and its face can be calculated subsequently. The main goal of the proposed new boundary method is to reach the boundary of an inscribed regular polygon in a circle. The study begins by drawing a regular polygon with three vertices. After that, the number of vertices increases without limit until describing a circle. Newton explains this concept also physics-mathematically. Today his method is very relevant as it is directly related to the computer and its graphic capabilities. The Java programming language and specifically the Java3D library were used to describe these results.

In the ceramic field the process of forming a ceramic body consists of several steps that must be executed efficiently and controlled closely to achieve the desired product. A major step in the process is the selection of raw materials, which not only will provide the necessary oxides, but also will melt and fine well to form a high-quality product. This process, if carried out on a trial-and-error manner, may lead to an uneconomical production cost due to wrong materials being selected. In addition, some important physical batch characteristics may be ignored owing to the increase in computational requirements if more constraints are added to the process. In this paper we propose the mathematical modelling approach, which has gained very little attention from researchers in this field, as an alternative to the trial-and-error approach. The model presented in this paper may be used to calculate the batch formula of a designed product without first knowing its empirical formula. An illustrated example of the use of this model is also provided.