000 02148 a2200289 4500
999 _c53485
_d53485
008 200924b ||||| |||| 00| 0 eng d
020 _a9780486601533
082 _a512.4
_bKNO
100 _aKnopp, Konrad
245 _aInfinite sequences and series
260 _bDover Publications,
_c1956.
_aNew York:
300 _av, 186 p.;
_bpb;
_c21 cm.
365 _aUSD
_b10.95
440 _aDover Books on Mathematics.
504 _aBibliography: p. 175-176.
520 _aOne of the finest expositors in the field of modern mathematics, Dr. Konrad Knopp here concentrates on a topic that is of particular interest to 20th-century mathematicians and students. He develops the theory of infinite sequences and series from its beginnings to a point where the reader will be in a position to investigate more advanced stages on his own. The foundations of the theory are therefore presented with special care, while the developmental aspects are limited by the scope and purpose of the book. All definitions are clearly stated; all theorems are proved with enough detail to make them readily comprehensible. The author begins with the construction of the system of real and complex numbers, covering such fundamental concepts as sets of numbers and functions of real and complex variables. In the treatment of sequences and series that follows, he covers arbitrary and null sequences; sequences and sets of numbers; convergence and divergence; Cauchy's limit theorem; main tests for sequences; and infinite series. Chapter three deals with main tests for infinite series and operating with convergent series. Chapters four and five explain power series and the development of the theory of convergence, while chapter six treats expansion of the elementary functions. The book concludes with a discussion of numerical and closed evaluation of series.
650 _aMathematics
650 _aAlgebra
650 _aPrerequisites
650 _aConvergent series
650 _aPower Series
650 _aElementary Functions
650 _aNumerical
650 _aComparison Tests
700 _aBagemihl, Frederick (Tr.)
942 _2ddc
_cTD