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Bonar D.D., Khoury M.J. — Real Infinite Series
Bonar D.D., Khoury M.J. — Real Infinite Series



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Название: Real Infinite Series

Авторы: Bonar D.D., Khoury M.J.

Аннотация:

This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers.

"Real Infinite Series" presents the theory of real infinite series, including elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Recognizing the interest in problem solving that abounds with students of mathematics, the authors devote a chapter to problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition.

The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals (what Martin Gardner calls "look-see" diagrams), and several fallacious proofs are made available.

Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works devoted entirely or partially to infinite series.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 264

Добавлена в каталог: 16.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, Niels      52 54
Abel-Dini Scale      52 105 183
Absolute convergence      35 36
Achilles      15
Alternating harmonic series      73
Alternating series      36
Alternating Series Test      37 39
Archytas of Tarentum      244
Associativity      19
Bernoulli, Jakob      69
Bernoulli, Johann      70
Bertrand Simplified      54
Bertrand's Tests      53
Bertrand's Tests, proven      58—64
Binomial theorem      60
Bois-Reymond      57
Bolyai, Farkas      48
Casting, Out Nines      81
Cauchy condensation test      43 66
Cauchy criterion sequence      21
Cauchy criterion series      41 43
Cauchy product      109 130 131
Cauchy sequence      21
Cauchy series      41 42 125
Cauchy — Schwartz inequality      90 146 180
Chain rule      59
Collapse      14
Commutativity of addition      18
Comparison Test      23 24 183
Completeness axiom      3
Conditional convergence      35 36 144
Converge sequence      2
Converge series      8
Converge to infinity      2
decimal      13
Dedekind      57
Degree      31
Differentiable function      39
Dini, Ulisse      52
Dirichlet      57
Diverge to infinity      2
Diverge, by oscillation      3
Diverge, sequence      2
Diverge, series      8
Divergence test      20 23 30 40
Divergence theorem      144
Domino stacking      86
Doubly-indexed sequence      143
Dover Publications      126
Dummy variable      2
Egyptian fraction      81
Empty product      58
Empty summation      58
Euler's constant      72 140
Eventually      21 24
Extrinsic test      29
Fallacies, Flaws, and Flimflam      193
Fundamental Theorem of Arithmetic      84
Fundamental theorem of calculus      22
Gabriel's Staircase      199
Gamma      72 140
Gauss' test      50 52
Gauss, Karl Friedrich      50
Geometric series      9 11 84
Greatest tower bound      4
Greedy algorithm      80
GROUPING      19 96 145
Hardy, Kenneth      126
Harmonic      65
Harmonic, progression      243
Harmonic, series      38
INDEX      2
Infinite product      83 84 132
Integral Comparison Test      186
Integral test      28 29 30 183
Integration by parts      54
Intermediate Value Theorem      189
INTRINSIC      29 53
Iterated logarithm      52
Kummer's test      46 50 51
Kummer's Test, simplified      47
Least upper bound      3
LIMIT      2
Limit Comparison Test      25 31 125
Limit Comparison Test, strengthened      26
Limit inferior      7
Limit superior      7
Logarithmic scales      52
Mean value theorem      60
Mengoli's Divergence Proof      69
Monotone decreasing      3
Monotone increasing      3
Monotonic      3
Nondecreasing      3
Nonincreasing      3
Octave      244
Oresme, Nicole      66
Oscillate      3
Oscillation      20
Overloading      18
Overshoot      76
P-series      30 32
Partial fraction      14
Partial sums      23
Pebbling problem      193
Positive series      22
Power series      103 108
Prime harmonic series      83
Primes, distribution      85
Principle of inclusion-exclusion      102
Product rule      59
Proper divergence      93
Putnam Competition      151
Pythagoreans      243
Raabe's test      48
Raabe, Ludwig      48
Rate of growth      72
Ratio Comparison Test      26 62
Ratio Test      32 33 49 98
Ratio Test, strengthened      33
Real infinite sequence      1
Real infinite series      8
Rearrangement      18 22 77 95 96 120
Regrouping      95
reordering      95
Repeating decimal      13
Root test      33
Root Test, strengthened      34
Schlomilch      44
Selective sums      79
Sequence of partial products      83
Sequence of partial sums      8
Sequence of terms      8
Squeeze principle      119
Strictly positive series      22
Subsequence      4
Subsequential limit point      4
Summation by parts      54 55
tail      9 23 42 56
Taylor series      74
Telescope      14
Telescoping series      13
Thin harmonic series      82
Undershoot      76
Unordered series      92 130
Williams, Kenneth      126
Zeno      65
Zeno's (First) Paradox      15
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