Tooling up mathematics for engineering
It has often been said that one of the primary objectives of Mathematics is to furnish tools to physicists and engineers for solution of their problems. It is evident from the history of the mathematical sciences that many fundamental mathematical discoveries have been initiated by the urge for understanding nature's laws and many mathematical methods have been invented by men primarily interested in practical applications. However, every true mathematician will feel that a restriction of mathematical research to problems which have immediate applications would be unfair to the "Queen of Sciences." As a matter of fact, the devoted "minnesingers" of the Queen have often revolted against degradation of their mistress to the position of a "handmaiden" of her more practical minded and temporarily more prosperous sisters. It is not difficult to understand the reasons for the controversial viewpoints of mathematicians and engineers. They have been pointed out more than once, by representatives of both professions. The mathematician says to the engineer-. I have built a building on a sound foundation: a system of theorems based on well defined postulates. I have delved into the analysis of the process of logical thinking to find out whether or not there are any statements which could be considered true or at least potentially true. I am interested in functional relations between entities which are well defined creations of my own mind and in methods which enable me to explore various aspects of such functional relations. If you find any of the concepts, logical processes or methods which I have developed useful for your daily work, I am certainly glad. All my results are at your disposal, but let me pursue my own objectives in my own way. Says the engineer: Your great forbears, who were mathematicians long before you, talked a different language. Did not Leonhard Euler distribute his time between discoveries in pure mathematics and in the theory of engineering devices? The fundamentals of the theory of turbines, the theory of buckling of columns, the theory of driving piles into soil were contributions of Euler. The development of mathematical analysis cannot be separated from the development of physics and especially of mechanics. It is doubtful whether a human mind would ever have conceived the idea of differential equations without the urge to find a mathematical tool for the computation