Tag: Introduction to calculus

1.5 Symbolic versus numerical calculus
Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to teaching calculus is based on manipulating symbols (variables) in equations, learning how different types of mathematical functions become transformed by the calculus operations of differentiation and integration. For example, suppose a firstsemester calculus student were given the following…

1.1 Introduction to calculus
Few areas of mathematics are as powerfully useful in describing and analyzing the physical world as calculus: the mathematical study of changes. Calculus also happens to be tremendously confusing to most students first encountering it. A great deal of this confusion stems from mathematicians’ insistence on rigor1 and denial of intuition. Look around you right now. Do…