Theory and Application of Infinite Series (Dover Books on Mathematics)

This classic work, written in a clear and interesting style, with many exercises, offers a thorough and reliable treatment of an important branch of higher analysis. It lends itself well to use in course work; however, because of its consistent clear illustrations of theoretical difficulties, the book is also ideal for self-study.Since all higher analysis depends on the theory of numbers, Professor Knopp (formerly Professor of Mathematics, University of Tübingen) begins with an introduction to the theory of real numbers, an indispensable foundation for what is to come. This introduction is followed by an extensive account of the theory of sequences and the actual theory of infinite series. The latter is covered in two stages: (1) the classical theory (2) later developments of the 19th century.Carefully selected exercises have been included throughout, emphasizing applications of the theory, rather than purely theoretical considerations.Aimed at students already acquainted with the elements of differential and integral calculus, this work grew out of the author's lectures and course work at the universities of Berlin and Königsberg. This pedagogical background helped him achieve a work of utmost clarity and precision — one that belongs in the library of every serious mathematician or student of higher analysis.