Calculus of one variable

The goal of this chapter is to present some calculus material needed for applying and developing techniques of artificial intelligence and machine learning. The first exercise set is a brief problem set with detailed solutions to help review some background material from calculus. The topics under the larger umbrella of calculus of real-valued functions, but focused on specific topics that arise naturally in the study of AI. It includes an in-depth look at the origins and uses of the exponential functions, including Gaussian functions and integrals, Fourier series and transforms. We also look at sigmoid functions and the gamma function as they arise as well. Each topic has worked examples or its own exercise set with solutions to move the reader to a better understanding of these tools.