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.
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978-0-8218-3345-2 (9780821833452)
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Schweitzer Klassifikation
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; 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
