Asymptotic Analysis and Perturbation Theory - Paulsen, William (Chapman & Hall, 2013)
This self-contained text makes the difficult subject of asymptotics easy to comprehend. It immediately introduces asymptotic notation and then applies this tool to familiar problems, including limits, inverse functions, and integrals. Along the way, the book explores the properties of some important functions in applied mathematics. Assuming no prior knowledge of differential equations, it explains the exact solution of only the simplest differential equations, such as first-order linear and separable equations.