This document provides examples and problems related to differential equations, difference equations, geometric sums, signal processing, signal decomposition, fluid dynamics modeling, and pharmacokinetic modeling. It includes 7 problems covering topics such as solving differential and difference equations, power series expansions, signal transformations, decomposing signals into even and odd parts, modeling coupled fluid tanks, and modeling drug dosing to understand variable initial dosing. For each problem, relevant concepts are explained and the reader is prompted to provide solutions, plots, or analyses.