Functions of Several Variables

Couverture
Springer Science & Business Media, 10 juin 1987 - 412 pages
The purpose of this book is to give a systematic development of differential and integral calculus for functions of several variables. The traditional topics from advanced calculus are included: maxima and minima, chain rule, implicit function theorem, multiple integrals, divergence and Stokes's theorems, and so on. However, the treatment differs in several important respects from the traditional one. Vector notation is used throughout, and the distinction is maintained between n-dimensional euclidean space En and its dual. The elements of the Lebesgue theory of integrals are given. In place of the traditional vector analysis in £3, we introduce exterior algebra and the calculus of exterior differential forms. The formulas of vector analysis then become special cases of formulas about differential forms and integrals over manifolds lying in P. The book is suitable for a one-year course at the advanced undergraduate level. By omitting certain chapters, a one semester course can be based on it. For instance, if the students already have a good knowledge of partial differentiation and the elementary topology of P, then substantial parts of Chapters 4, 5, 7, and 8 can be covered in a semester. Some knowledge of linear algebra is presumed. However, results from linear algebra are reviewed as needed (in some cases without proof). A number of changes have been made in the first edition. Many of these were suggested by classroom experience. A new Chapter 2 on elementary topology has been added.
 

Table des matières

I
1
II
2
III
5
IV
10
V
14
VI
19
VII
28
VIII
31
XLVII
227
XLVIII
237
XLIX
240
L
245
LI
247
LII
253
LIII
258
LIV
265

IX
37
X
43
XI
47
XII
50
XIII
56
XIV
60
XV
62
XVI
67
XVII
70
XVIII
76
XXI
79
XXII
82
XXIII
89
XXIV
99
XXV
107
XXVI
119
XXIX
125
XXX
128
XXXI
134
XXXII
140
XXXIII
147
XXXIV
153
XXXV
161
XXXVI
167
XXXVII
168
XXXVIII
170
XXXIX
181
XL
186
XLI
190
XLII
200
XLIII
206
XLIV
209
XLV
216
XLVI
222
LV
268
LVI
275
LVII
276
LVIII
283
LIX
287
LX
291
LXI
295
LXII
306
LXIII
309
LXIV
311
LXV
316
LXVI
318
LXVII
321
LXVIII
322
LXIX
329
LXX
334
LXXI
340
LXXII
350
LXXIII
353
LXXIV
356
LXXV
362
LXXVI
367
LXXVII
369
LXXVIII
375
LXXIX
380
LXXX
383
LXXXI
385
LXXXII
386
LXXXIII
388
LXXXIV
389
LXXXV
391
LXXXVI
405
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