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020			_a9780429275166 _q(electronic bk.)
020			_a0429275161 _q(electronic bk.)
020			_a9780415000352 _q(electronic bk.)
020			_a0415000351 _q(electronic bk.)
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020			_a9781000000351
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035			_a(OCoLC)1097665040 _z(OCoLC)1097959693 _z(OCoLC)1097985226
035			_a(OCoLC-P)1097665040
050		4	_aQA331.7 _b.K732 2019eb
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072		7	_aMAT _x034000 _2bisacsh
072		7	_aPBK _2bicssc
082	0	4	_a515/.9 _223
100	1		_aKrantz, Steven G. _q(Steven George), _d1951- _eauthor. _912173
245	1	0	_aComplex variables : _ba physical approach with applications / _cSteven G. Krantz.
250			_aSecond edition.
264		1	_aBoca Raton : _bCRC Press, _c[2019]
300			_a1 online resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aTextbooks in mathematics
505	0		_aCover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface to the Second Edition for the Instructor; Preface to the Second Edition for the Student; Preface to the First Edition; 1: Basic Ideas; 1.1 Complex Arithmetic; 1.1.1 The Real Numbers; 1.1.2 The Complex Numbers; 1.1.3 Complex Conjugate; Exercises; 1.2 Algebraic and Geometric Properties; 1.2.1 Modulus of a Complex Number; 1.2.2 The Topology of the Complex Plane; 1.2.3 The Complex Numbers as a Field; 1.2.4 The Fundamental Theorem of Algebra; Exercises; 2: The Exponential and Applications
505	8		_a2.1 The Exponential Function2.1.1 Laws of Exponentiation; 2.1.2 The Polar Form of a Complex Number; Exercises; 2.1.3 Roots of Complex Numbers; 2.1.4 The Argument of a Complex Number; 2.1.5 Fundamental Inequalities; Exercises; 3: Holomorphic and Harmonic Functions; 3.1 Holomorphic Functions; 3.1.1 Continuously Differentiable and Ck Functions; 3.1.2 The Cauchy-Riemann Equations; 3.1.3 Derivatives; 3.1.4 Definition of Holomorphic Function; 3.1.5 Examples of Holomorphic Functions; 3.1.6 The Complex Derivative; 3.1.7 Alternative Terminology for Holomorphic Functions; Exercises
505	8		_a3.2 Holomorphic and Harmonic Functions3.2.1 Harmonic Functions; 3.2.2 Holomorphic and Harmonic Functions; Exercises; 3.3 Complex Differentiability; 3.3.1 Conformality; Exercises; 4: The Cauchy Theory; 4.1 Real and Complex Line Integrals; 4.1.1 Curves; 4.1.2 Closed Curves; 4.1.3 Differentiable and Ck Curves; 4.1.4 Integrals on Curves; 4.1.5 The Fundamental Theorem of Calculus along Curves; 4.1.6 The Complex Line Integral; 4.1.7 Properties of Integrals; Exercises; 4.2 The Cauchy Integral Theorem; 4.2.1 The Cauchy Integral Theorem, Basic Form; 4.2.2 More General Forms of the Cauchy Theorem
505	8		_a4.2.3 Deformability of Curves4.2.4 Cauchy Integral Formula, Basic Form; 4.2.5 More General Versions of the Cauchy Formula; Exercises; 4.3 Variants of the Cauchy Formula; 4.4 The Limitations of the Cauchy Formula; Exercises; 5: Applications of the Cauchy Theory; 5.1 The Derivatives of a Holomorphic Function; 5.1.1 A Formula for the Derivative; 5.1.2 The Cauchy Estimates; 5.1.3 Entire Functions and Liouville's Theorem; 5.1.4 The Fundamental Theorem of Algebra; 5.1.5 Sequences of Holomorphic Functions and Their Derivatives; 5.1.6 The Power Series Representation of a Holomorphic Function
505	8		_a5.1.7 Table of Elementary Power SeriesExercises; 5.2 The Zeros of a Holomorphic Function; 5.2.1 The Zero Set of a Holomorphic Function; 5.2.2 Discrete Sets and Zero Sets; 5.2.3 Uniqueness of Analytic Continuation; Exercises; 6: Isolated Singularities; 6.1 Behavior Near an Isolated Singularity; 6.1.1 Isolated Singularities; 6.1.2 A Holomorphic Function on a Punctured Domain; 6.1.3 Classification of Singularities; 6.1.4 Removable Singularities, Poles, and Essential Singularities; 6.1.5 The Riemann Removable Singularities Theorem; 6.1.6 The Casorati-Weierstrass Theorem; 6.1.7 Concluding Remarks
520			_aWeb Copy The idea of complex numbers dates back at least 300 years--to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.
588			_aOCLC-licensed vendor bibliographic record.
650		0	_aFunctions of complex variables. _912174
650		0	_aFunctions of complex variables _vTextbooks. _912175
650		0	_aNumbers, Complex _vTextbooks. _912176
650		0	_aMathematical analysis _vTextbooks. _912177
650		7	_aMATHEMATICS / Calculus. _2bisacsh _95469
650		7	_aMATHEMATICS / Mathematical Analysis. _2bisacsh _95470
856	4	0	_3Taylor & Francis _uhttps://www.taylorfrancis.com/books/9780429275166
856	4	2	_3OCLC metadata license agreement _uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942			_cEBK
999			_c70164 _d70164