ABSTRACT
This chapter considers some applications of integration and differential equations (DEs) in context and how to solve some problems associated with these. However, it is important, as in all areas of mathematics, to try to help students understand the conceptual base of the topic and to ensure that the rules can be correctly applied. The degree or order of a DE is the order of the highest derivative in it. Over the centuries solving DEs has exercised the minds of many mathematicians and solutions have been found to many different types of DEs. Indeed, solving them continues to be an important area of mathematical research. The fact that each DE gives rise to an infinite family of solution functions can be seen by plotting what is called a slope (or direction) field. Digital technology is extremely useful for plotting slope fields. There are more accurate numerical approximations to solutions of DEs based on Euler’s method that are commonly used.
