A Review on Mathematics for Engineers: Fundamentals and Applications

Abstract

This review article addresses the topic of mathematics for engineers, considering its fundamentals and applications. Mathematics is framed as the language of engineering. The educational objectives of the document consist of clarifying some concepts and using simple examples, problems, and solutions. At the end of the review, the issues addressed are summarized, and some additional considerations on this matter are made. Mathematics is an abstract science that involves the study of numbers, quantities, structures, and shapes and their relationships in different contexts. A possible division of mathematics can be into pure and applied mathematics. Pure mathematics concerns mathematical conceptions and relationships without any relation to real life or practical problems, whereas applied mathematics refers to math that has a practical goal, i.e., applying mathematics to problems of nature and engineering. It can be said that science and technology are based on mathematics; therefore, nothing that involves knowledge or creates new knowledge can be dissociated from math. In this way, engineering is mathematics, as engineering is the creation and fabrication of artifacts by converting an idea (an abstraction) into matter (a tangible); general mathematical models (equations), specific parameters (problems), mathematical computer simulations (calculations), and experiments (testing).