N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland, 1958 (Bibliotheca Mathematica vol. IV). The classic short course on asymptotic expansions: the O and o calculus, implicit functions, summation by Euler’s formula, Laplace’s method, saddle points, the method of stationary phase, iterated functions and differential equations. A 1958 hardcover copy.