ASYMPTOTIC METHODS IN ANALYSIS

Part of the attraction of this book is its pleasant, straightforward style of exposition, leavened with a touch of humor and occasionally even using the dramatic form of dialogue. The book begins with a general introduction (fundamental to the whole book) on O and o notation and asymptotic series in general. Subsequent chapters cover estimation of implicit functions and the roots of equations; various methods of estimating sums; extensive treatment of the saddle-point method with full details and intricate worked examples; a brief introduction to Tauberian theorems; a detailed chapter on iteration; and a short chapter on asymptotic behavior of solutions of differential equations. Most chapters progress from simple examples to difficult problems; and in some cases, two or more different treatments of the same problem are given to enable the reader to compare different methods. Several proofs of the Stirling theorem are included, for example, and the problem of the iterated sine is treated twice in Chapter 8. Exercises are given at the end of each chapter.