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Complex variables and applications:

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Bibliographic Details
Main Authors:	Brown, James Ward 1934- (Author), Churchill, Ruel Vance 1899-1987 (Author)
Format:	Book
Language:	English
Published:	Boston [u.a.] McGraw-Hill c2009
Edition:	8th ed.
Series:	Brown and Churchill series
Subjects:	Funções de uma variável complexa (análise;textos elementares) Functions of complex variables Funktionentheorie Mehrere komplexe Variable Funktion > Mathematik
Online Access:	Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	XI, 468 S.
ISBN:	9780073051949 0073051942

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MARC


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adam_text	CONTENTS Preface 1 Complex Numbers Sums and Products 1 Basic Algebraic Properties 3 Further Properties 5 Vectors and Moduli 9 Complex Conjugates 13 Exponential Form 16 Products and Powers in Exponential Form 18 Arguments of Products and Quotients 20 Roots of Complex Numbers 24 Examples 27 Regions in the Complex Plane 31 2 Analytic Functions 35 Functions of a Complex Variable 35 Mappings 38 Mappings by the Exponential Function 42 Limits 45 Theorems on Limits 48 VI CONTENTS Limits Involving the Point at Infinity 50 Continuity 53 Derivatives 56 Differentiation Formulas 60 Cauchy-Riemann Equations 63 Sufficient Conditions for Differentiability 66 Polar Coordinates 68 Analytic Functions 73 Examples 75 Harmonic Functions 78 Uniquely Determined Analytic Functions 83 Reflection Principle 85 3 Elementary Functions 89 The Exponential Function 89 The Logarithmic Function 93 Branches and Derivatives of Logarithms 95 Some Identities Involving Logarithms 98 Complex Exponents 101 Trigonometric Functions 104 Hyperbolic Functions 109 Inverse Trigonometric and Hyperbolic Functions 112 4 Integrals 117 Derivatives of Functions wit) 117 Definite Integrals of Functions w(t) 119 Contours 122 Contour Integrals 127 Some Examples 129 Examples with Branch Cuts 133 Upper Bounds for Moduli of Contour Integrals 137 Antiderivatives 142 Proof of the Theorem 146 Cauchy-Goursat Theorem 150 Proof of the Theorem 152 CONTENTS VU Simply Connected Domains 156 Multiply Connected Domains 158 Cauchy Integral Formula 164 An Extension of the Cauchy Integral Formula 165 Some Consequences of the Extension 168 Liouville s Theorem and the Fundamental Theorem of Algebra 172 Maximum Modulus Principle 175 5 Series 181 Convergence of Sequences 181 Convergence of Series 184 Taylor Series 189 Proof of Taylor s Theorem 190 Examples 192 Laurent Series 197 Proof of Laurent s Theorem 199 Examples 202 Absolute and Uniform Convergence of Power Series 208 Continuity of Sums of Power Series 211 Integration and Differentiation of Power Series 213 Uniqueness of Series Representations 217 Multiplication and Division of Power Series 222 6 Residues and Poles 229 Isolated Singular Points 229 Residues 231 Cauchy s Residue Theorem 234 Residue at Infinity 237 The Three Types of Isolated Singular Points 240 Residues at Poles 244 Examples 245 Zeros of Analytic Functions 249 Zeros and Poles 252 Behavior of Functions Near Isolated Singular Points 257 VIU CONTENTS 7 Applications of Residues 261 Evaluation of Improper Integrals 261 Example 264 Improper Integrals from Fourier Analysis 269 Jordan s Lemma 272 Indented Paths 277 An Indentation Around a Branch Point 280 Integration Along a Branch Cut 283 Definite Integrals Involving Sines and Cosines 288 Argument Principle 291 Rouché s Theorem 294 Inverse Laplace Transforms 298 Examples 301 8 Mapping by Elementary Functions 311 Linear Transformations 311 The Transformation w = l/z 313 Mappings by l/z 315 Linear Fractional Transformations 319 An Implicit Form 322 Mappings of the Upper Half Plane 325 The Transformation w = sin z 330 Mappings by z2 and Branches of zl/2 336 Square Roots of Polynomials 341 Riemann Surfaces 347 Surfaces for Related Functions 351 9 Conformai Mapping 355 Preservation of Angles 355 Scale Factors 358 Local Inverses 360 Harmonic Conjugates 363 Transformations of Harmonic Functions 365 Transformations of Boundary Conditions 367 CONTENTS IX 10 Applications of Conformai Mapping 373 Steady Temperatures 373 Steady Temperatures in a Half Plane 375 A Related Problem 377 Temperatures in a Quadrant 379 Electrostatic Potential 385 Potential in a Cylindrical Space 386 Two-Dimensional Fluid Flow 391 The Stream Function 393 Flows Around a Corner and Around a Cylinder 395 11 The Schwarz-Christoffel Transformation 403 Mapping the Real Axis Onto a Polygon 403 Schwarz-Christoffel Transformation 405 Triangles and Rectangles 408 Degenerate Polygons 413 Huid Flow in a Channel Through a Slit 417 Flow in a Channel With an Offset 420 Electrostatic Potential About an Edge of a Conducting Plate 422 12 Integral Formulas of the Poisson Type 429 Poisson Integral Formula 429 Dirichlet Problem for a Disk 432 Related Boundary Value Problems 437 Schwarz Integral Formula 440 Dirichlet Problem for a Half Plane 441 Neumann Problems 445 Appendixes 449 Bibliography 449 Table of Transformations of Regions 452 Index 461
adam_txt	CONTENTS Preface 1 Complex Numbers Sums and Products 1 Basic Algebraic Properties 3 Further Properties 5 Vectors and Moduli 9 Complex Conjugates 13 Exponential Form 16 Products and Powers in Exponential Form 18 Arguments of Products and Quotients 20 Roots of Complex Numbers 24 Examples 27 Regions in the Complex Plane 31 2 Analytic Functions 35 Functions of a Complex Variable 35 Mappings 38 Mappings by the Exponential Function 42 Limits 45 Theorems on Limits 48 VI CONTENTS Limits Involving the Point at Infinity 50 Continuity 53 Derivatives 56 Differentiation Formulas 60 Cauchy-Riemann Equations 63 Sufficient Conditions for Differentiability 66 Polar Coordinates 68 Analytic Functions 73 Examples 75 Harmonic Functions 78 Uniquely Determined Analytic Functions 83 Reflection Principle 85 3 Elementary Functions 89 The Exponential Function 89 The Logarithmic Function 93 Branches and Derivatives of Logarithms 95 Some Identities Involving Logarithms 98 Complex Exponents 101 Trigonometric Functions 104 Hyperbolic Functions 109 Inverse Trigonometric and Hyperbolic Functions 112 4 Integrals 117 Derivatives of Functions wit) 117 Definite Integrals of Functions w(t) 119 Contours 122 Contour Integrals 127 Some Examples 129 Examples with Branch Cuts 133 Upper Bounds for Moduli of Contour Integrals 137 Antiderivatives 142 Proof of the Theorem 146 Cauchy-Goursat Theorem 150 Proof of the Theorem 152 CONTENTS VU Simply Connected Domains 156 Multiply Connected Domains 158 Cauchy Integral Formula 164 An Extension of the Cauchy Integral Formula 165 Some Consequences of the Extension 168 Liouville's Theorem and the Fundamental Theorem of Algebra 172 Maximum Modulus Principle 175 5 Series 181 Convergence of Sequences 181 Convergence of Series 184 Taylor Series 189 Proof of Taylor' s Theorem 190 Examples 192 Laurent Series 197 Proof of Laurent's Theorem 199 Examples 202 Absolute and Uniform Convergence of Power Series 208 Continuity of Sums of Power Series 211 Integration and Differentiation of Power Series 213 Uniqueness of Series Representations 217 Multiplication and Division of Power Series 222 6 Residues and Poles 229 Isolated Singular Points 229 Residues 231 Cauchy's Residue Theorem 234 Residue at Infinity 237 The Three Types of Isolated Singular Points 240 Residues at Poles 244 Examples 245 Zeros of Analytic Functions 249 Zeros and Poles 252 Behavior of Functions Near Isolated Singular Points 257 VIU CONTENTS 7 Applications of Residues 261 Evaluation of Improper Integrals 261 Example 264 Improper Integrals from Fourier Analysis 269 Jordan's Lemma 272 Indented Paths 277 An Indentation Around a Branch Point 280 Integration Along a Branch Cut 283 Definite Integrals Involving Sines and Cosines 288 Argument Principle 291 Rouché's Theorem 294 Inverse Laplace Transforms 298 Examples 301 8 Mapping by Elementary Functions 311 Linear Transformations 311 The Transformation w = l/z 313 Mappings by l/z 315 Linear Fractional Transformations 319 An Implicit Form 322 Mappings of the Upper Half Plane 325 The Transformation w = sin z 330 Mappings by z2 and Branches of zl/2 336 Square Roots of Polynomials 341 Riemann Surfaces 347 Surfaces for Related Functions 351 9 Conformai Mapping 355 Preservation of Angles 355 Scale Factors 358 Local Inverses 360 Harmonic Conjugates 363 Transformations of Harmonic Functions 365 Transformations of Boundary Conditions 367 CONTENTS IX 10 Applications of Conformai Mapping 373 Steady Temperatures 373 Steady Temperatures in a Half Plane 375 A Related Problem 377 Temperatures in a Quadrant 379 Electrostatic Potential 385 Potential in a Cylindrical Space 386 Two-Dimensional Fluid Flow 391 The Stream Function 393 Flows Around a Corner and Around a Cylinder 395 11 The Schwarz-Christoffel Transformation 403 Mapping the Real Axis Onto a Polygon 403 Schwarz-Christoffel Transformation 405 Triangles and Rectangles 408 Degenerate Polygons 413 Huid Flow in a Channel Through a Slit 417 Flow in a Channel With an Offset 420 Electrostatic Potential About an Edge of a Conducting Plate 422 12 Integral Formulas of the Poisson Type 429 Poisson Integral Formula 429 Dirichlet Problem for a Disk 432 Related Boundary Value Problems 437 Schwarz Integral Formula 440 Dirichlet Problem for a Half Plane 441 Neumann Problems 445 Appendixes 449 Bibliography 449 Table of Transformations of Regions 452 Index 461
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author	Brown, James Ward 1934- Churchill, Ruel Vance 1899-1987
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edition	8th ed.
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spelling	Brown, James Ward 1934- Verfasser (DE-588)136655386 aut Complex variables and applications James Ward Brown ; Ruel V. Churchill 8th ed. Boston [u.a.] McGraw-Hill c2009 XI, 468 S. txt rdacontent n rdamedia nc rdacarrier Brown and Churchill series Includes bibliographical references and index Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Funktion Mathematik (DE-588)4071510-3 s 1\p DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 2\p DE-604 Churchill, Ruel Vance 1899-1987 Verfasser (DE-588)115367608 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Brown, James Ward 1934- Churchill, Ruel Vance 1899-1987 Complex variables and applications Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd
subject_GND	(DE-588)4018935-1 (DE-588)4169285-8 (DE-588)4071510-3
title	Complex variables and applications
title_auth	Complex variables and applications
title_exact_search	Complex variables and applications
title_exact_search_txtP	Complex variables and applications
title_full	Complex variables and applications James Ward Brown ; Ruel V. Churchill
title_fullStr	Complex variables and applications James Ward Brown ; Ruel V. Churchill
title_full_unstemmed	Complex variables and applications James Ward Brown ; Ruel V. Churchill
title_short	Complex variables and applications
title_sort	complex variables and applications
topic	Funções de uma variável complexa (análise;textos elementares) larpcal Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd
topic_facet	Funções de uma variável complexa (análise;textos elementares) Functions of complex variables Funktionentheorie Mehrere komplexe Variable Funktion Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016275421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT brownjamesward complexvariablesandapplications AT churchillruelvance complexvariablesandapplications

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