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's transformation and Gibbs's phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.

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
• 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