2.2 Physics and Calculus


The State of nature at a given point in time could be fixed via a photographic snapshot and described with words. In a mathematical and physical picture this would correspond to a description of nature via formulas in which the time does not appear. Thus already many states, for example equilibria, can be described via simple mathematical equations.

In addition Physics examines and describes changes in nature, 2 and a rule these changes happen as function of time. This provides its theories the ability to understand the development of a current state from its conditions at an earlier point in time. More important is the ability to predict a future state from the knowledge of the current state; this ability empowers the techniques based on it to achieve a desired,future effect.

For the deeper understanding and practical application of physics the knowledge of differential calculus is necessary, since the changes (derivatives) and the sum of their effects (integrals) have to be considered. Without this understanding physics becomes a collection of more or less disconnected formulas, which are only applicable to very limited cases. Thus the calculation of results becomes a nuisance for the students at schools, which blocks their insight into the simplicity and beauty of the relationships of mathematics, physics and technology.

But the mathematical operations and methods that are needed for the basic understanding of the subject are not really difficult. Using suitable visualizations the notions used can be easily grasped. Using the computer for the calculation and for creating the visualization media (diagrams, animations, simulations) it becomes easy to to put this into practice. End of chapter 2.