By Roger B. Nelsen

A thespian or cinematographer may well outline a *cameo* as a short visual appeal of a recognized determine, whereas a gemologist or lapidary may possibly outline it as a useful or semiprecious stone. This e-book provides fifty brief improvements or supplementations (the Cameos) for the first-year calculus path within which a geometrical determine in brief seems. a number of the Cameos illustrate mainstream issues resembling the by-product, combinatorial formulation used to compute Riemann sums, or the geometry at the back of many geometric sequence. different Cameos current themes obtainable to scholars on the calculus point yet now not frequently encountered within the direction, similar to the Cauchy-Schwarz inequality, the mathematics mean-geometric suggest inequality, and the Euler-Mascheroni constant.

There are fifty Cameos within the ebook, grouped into 5 sections: half I Limits and Differentiation; half II Integration; half III endless sequence; half IV extra subject matters, and half V Appendix: a few Precalculus issues. the various Cameos contain workouts, so suggestions to the entire workouts follows half V. The e-book concludes with References and an Index.

Many of the Cameos are tailored from articles released in journals of the MAA, akin to *The American Mathematical Monthly*, *Mathematics Magazine*, and *The collage arithmetic Journal*. a few come from different mathematical journals, and a few have been created for this booklet. via accumulating the Cameos right into a ebook we are hoping that they are going to be extra obtainable to lecturers of calculus, either to be used within the lecture room and as supplementary explorations for students.