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When the first edition of my Course of Modem Analysis became exhausted, and theS yndics of the Press invited me to prepare a second edition, I determined to introduce many new features into the work. The pressure of other duties prevented me for some time from carrying out this plan, and it seemed as if the appearance of the new edition might be indefinitely postponed. At this juncture, my friend and former pupil, Mr G. N. Watson, offered to share the work of preparation; and, with his cooperation, it has now been completed. The appearance of several treatises on the Theory of Convergence, such as Mr Hardy sC ourse of Pure Mathematics and, more particularly, Dr Bromwich sT heory of Infinite Series, led us to consider the desirability of omitting the first four chapters of this work; but we finally decided to retain all that was necessary for subsequent developments, in order to make the book complete in itself. The concise account which will be found in these chapters is by no means exhaustive, although we believe it to be fairly complete. For the discussion of Infinite Series on their own merits, we may refer to the work of Dr Bromwich. The new chapters on Riemann I ntegration, on Integral Equations, and on the Riemann Zeta-F unction, are entirely due toM rW atson :he has revised and improved the new chapters which I had myself drafted and he has enlarged or partly rewritten much of the matter which appeared in the original work. It is therefore fitting that our names should stand together on the title-page. Grateful acknowledgment must be made toM rW. H. A. Lawrence, B.A., and Mr C. E. Winn, B.A., Scholars ofT rinity College, who with great kindness and care have read the proof-sheets, toM iss Wrinch, Scholar of Girton College, who assisted in preparing the index, and toM rL ittlewood, who read the early chapters in manuscript and made many helpful critici
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