The integral symbol, , in the heading for this section indicates that it is meant to be read by students in calculus-based physics. Stu- dents in an algebra-based physics course should skip these sections. The calculus-related sections in this book are meant to be usable by students who are taking calculus concurrently, so at this early point in the physics course I do not assume you know any calculus yet. This section is therefore not much more than a quick preview of calculus, to help you relate what you’re learning in the two courses. |
Newton was the rst person to gure out the tangent-line de - |
nition of velocity for cases where the x - t graph is nonlinear. Be- fore Newton, nobody had conceptualized the description of motion in terms of x - t and v - t graphs. In addition to the graphical techniques discussed in this chapter, Newton also invented a set of symbolic techniques called calculus. If you have an equation for x |
in terms of t, calculus allows you, for instance, to nd an equation for v in terms of t. In calculus terms, we say that the function v(t) is the derivative of the function x(t). In other words, the derivative of a function is a new function that tells how rapidly the original function was changing. We now use neither Newton’s name for his technique (he called it “the method of uxions”) nor his notation. The more commonly used notation is due to Newton’s German con- temporary Leibnitz, whom the English accused of plagiarizing the calculus from Newton. In the Leibnitz notation, we write |