This chapter is largely concerned with vector-valued functions. In the first section, we introduce some of the basic geometry and computational methods for paths in the plane and space. This will be an important ingredient for the chain rule treated in the next chapter. We continue our study of paths in the second section, adding applications of Newton’s second law. Then we study arc length of paths.
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\(\ldots\) who by vigor of mind almost divine, the motions and figures of the planets, the paths of comets, and the tides of the seas first demonstrated.
—Newton’s Epitaph