AMS Chelsea Publishing 1926; 535 pp; hardcover Volume: 335 ISBN10: 0821839764 ISBN13: 9780821839768 List Price: US$65 Member Price: US$58.50 Order Code: CHEL/335.H
 This edition consists largely of a reproduction of the first edition (which was based on lectures on Elementary Analysis given at Queen's College, Galway, from 19021907), with additional theorems and examples. Additional material includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; a discussion of trigonometrical series, including Stokes's transformation and Gibbs's phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms. Reviews "The book is especially good at counterexamples, and includes many of these to warn against pitfalls in reasoning and to show that all the hypotheses of the theorems are really needed. One especially nice feature is the use of Tannery's theorem, on interchanging limit and summation, throughout the book."  MAA Reviews Table of Contents  Sequences and limits
 Series of positive terms
 Series in general
 Absolute convergence
 Double series
 Infinite products
 Series of variable terms
 Power series
 Special power series
 Trigonometrical formulae
 Complex series and products
 Special complex series and functions
 Nonconvergent series
 Asymptotic series
 Trigonometrical series
 Appendix I. Arithmetic theory of irrational numbers and limits
 Appendix II. Definitions of the logarithmic and exponential functions
 Appendix III. Some theorems on infinite integrals and gammafunctions
 Miscellaneous examples
 Index of special integrals, products, and series
 General index
