A First Course in Calculus

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Springer Science & Business Media, Mar 16, 1998 - Mathematics - 731 pages
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The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them. The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. One writes an advanced monograph for oneself, because one wants to give permanent form to one's vision of some beautiful part of mathematics, not otherwise ac cessible, somewhat in the manner of a composer setting down his sym phony in musical notation. This book is written for the students to give them an immediate, and pleasant, access to the subject. I hope that I have struck a proper com promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject. In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course. Rigor. This does not mean that so-called rigor has to be abandoned.
 

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Contents

II
3
III
5
IV
14
V
18
VI
21
VII
24
IX
29
X
34
LX
326
LXI
329
LXII
335
LXIII
341
LXIV
347
LXV
357
LXVI
371
LXVII
379

XI
35
XII
36
XIII
40
XIV
45
XV
51
XVI
55
XVII
57
XVIII
62
XIX
69
XX
76
XXI
79
XXII
91
XXIII
102
XXIV
104
XXV
106
XXVI
117
XXVII
124
XXVIII
132
XXIX
136
XXX
141
XXXI
147
XXXII
150
XXXIII
159
XXXIV
165
XXXV
176
XXXVI
181
XXXVII
188
XXXVIII
191
XXXIX
197
XL
202
XLI
216
XLII
222
XLIII
225
XLIV
230
XLV
236
XLVI
247
XLVII
256
XLVIII
262
XLIX
267
L
275
LI
278
LII
285
LIII
287
LIV
291
LV
292
LVI
296
LVII
308
LVIII
312
LIX
319
LXVIII
381
LXIX
387
LXX
390
LXXI
397
LXXII
408
LXXIII
415
LXXIV
419
LXXV
425
LXXVI
427
LXXVII
435
LXXVIII
437
LXXIX
447
LXXX
449
LXXXI
456
LXXXII
459
LXXXIII
468
LXXXIV
473
LXXXV
476
LXXXVI
480
LXXXVII
482
LXXXVIII
486
LXXXIX
489
XC
495
XCI
501
XCIII
502
XCIV
504
XCV
514
XCVI
517
XCVII
521
XCVIII
523
XCIX
531
C
534
CI
537
CII
552
CIII
556
CIV
565
CV
578
CVI
582
CVII
586
CVIII
593
CIX
599
CX
604
CXI
611
CXII
615
CXIII
621
CXIV
1
CXV
101
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