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 1902-1907), 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' transformation and Gibbs' phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.
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 Non-convergent 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 gamma-functions Miscellaneous examples Index of special integrals, products, and series General index.