You're looking for a helpful report on "Calculus Gems" by George B. Simmons in PDF format. Here's what I found:
: A collection of 26 "nuggets" or essays on specific mathematical results from number theory, geometry, and science. These are arranged to roughly follow the order of a standard calculus curriculum and include topics like: The divergence of the sum of reciprocals of all primes. Euler’s result on the sum of the reciprocals of squares. A simple approach to using relativistic mass. Why It Is Considered "Better" calculus gems simmons pdf better
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It covers topics often skipped in standard courses, such as the brachistochrone problem, the catenary, and complex series, providing a bridge between introductory calculus and advanced analysis. These are arranged to roughly follow the order