Complex Analysis (Google eBook)

Front Cover
Springer Science & Business Media, 1997 - Mathematics - 294 pages
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This unusually lively textbook on complex variables introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. Complex Analysis offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. Stressing motivation and technique, and containing a large number of problems and their solutions, this volume may be used as a text both in classrooms and for self-study. Topics covered include: The complex numbers; functions of a complex variable; analytic functions; line integrals and entire functions; properties of entire functions and of analytic functions; simply connected domains; isolated singularities; the residue theorem and applications; contour integral techniques; conformal mapping and the riemann mapping theorem; maximum-modulus theorems for unbounded domains; harmonic functions; forms of analytic functions; analytic continuation; the gamma and zeta functions; application to other areas of mathematics. For this second edition, the authors have revised some of the existing material and have provided new exercises and solution
  

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Contents

II
1
III
2
IV
4
V
10
VI
15
VII
17
VIII
20
IX
21
XXXIX
139
XL
146
XLI
149
XLII
152
XLIII
156
XLIV
157
XLV
163
XLVI
175

X
25
XI
27
XII
31
XIII
34
XIV
39
XV
43
XVI
50
XVII
54
XVIII
56
XIX
62
XX
64
XXI
67
XXII
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XXIII
73
XXIV
78
XXV
80
XXVI
85
XXVII
90
XXVIII
92
XXIX
99
XXX
101
XXXI
103
XXXII
107
XXXIII
113
XXXIV
115
XXXV
121
XXXVI
127
XXXVII
130
XLVII
178
XLVIII
183
XLIX
188
L
190
LI
193
LII
199
LIII
200
LIV
208
LV
213
LVI
215
LVII
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LVIII
226
LIX
228
LX
235
LXI
241
LXII
243
LXIV
244
LXV
245
LXVI
247
LXVII
249
LXVIII
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LXIX
256
LXX
257
LXXI
258
LXXII
263
LXXIII
290
LXXIV
291
Copyright

Common terms and phrases

Popular passages

Page 2 - A complex number is any number that can be written in the form a + bi, where a and b are real numbers, and i...
Page 1 - In the geometric representation, he wrote, one finds the "intuitive meaning of complex numbers completely established and more is not needed to admit these quantities into the domain of arithmetic.
Page 2 - С is the set of ordered pairs of real numbers (a, b) with addition and multiplication defined by (a, b) + (c, d) = (a + c, b + d} (a, fo)(c, if) = (ac - bd, ad + foe).
Page 1 - Euler, too, felt that complex numbers "exist only in the imagination" and considered complex roots of an equation useful only in showing that the equation actually has no solutions.

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About the author (1997)

Newman-Temple University, Philadephia, PA and Bar Elan University, Israel

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