A Concrete Approach to Classical Analysis

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Springer Science & Business Media, Nov 6, 2008 - Mathematics - 433 pages
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Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science.

The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems.

The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.

 

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Contents

I
1
II
3
III
6
IV
11
VI
12
VII
20
VIII
25
IX
30
LXX
207
LXXI
208
LXXII
214
LXXIII
216
LXXIV
217
LXXV
219
LXXVI
222
LXXVII
225

X
31
XI
32
XII
40
XIII
41
XV
44
XVI
48
XVII
49
XVIII
51
XIX
57
XX
65
XXI
70
XXIII
73
XXV
76
XXVI
77
XXVII
80
XXVIII
81
XXIX
82
XXX
85
XXXI
88
XXXII
94
XXXIII
98
XXXIV
108
XXXV
110
XXXVI
113
XXXVII
123
XXXVIII
125
XXXIX
126
XL
130
XLI
134
XLII
137
XLIII
138
XLIV
139
XLVI
144
XLVII
146
XLVIII
152
L
155
LI
156
LII
160
LIII
161
LV
164
LVI
165
LVII
167
LVIII
169
LIX
173
LX
177
LXI
183
LXII
184
LXIII
186
LXIV
189
LXV
191
LXVII
197
LXVIII
201
LXIX
206
LXXVIII
228
LXXIX
230
LXXX
231
LXXXII
235
LXXXIII
237
LXXXIV
239
LXXXV
242
LXXXVI
244
LXXXVII
247
LXXXVIII
249
LXXXIX
251
XCI
252
XCII
262
XCIII
263
XCIV
271
XCV
275
XCVI
278
XCVII
280
XCVIII
283
XCIX
284
C
287
CI
288
CII
296
CIII
304
CIV
312
CV
316
CVI
317
CVII
322
CIX
325
CX
333
CXI
341
CXII
346
CXIII
349
CXIV
353
CXV
354
CXVI
355
CXVII
356
CXVIII
358
CXIX
363
CXX
372
CXXI
374
CXXII
377
CXXIII
378
CXXIV
380
CXXV
384
CXXVI
390
CXXVII
409
CXXVIII
411
CXXIX
418
CXXX
423
CXXXI
425
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