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Previous Title:	Churchill Introduction to complex varaibles and applications
Main Authors:	Churchill, Ruel Vance 1899-1987 (Author), Brown, James Ward 1934- (Author), Verhey, Roger F. (Author)
Format:	Book
Language:	English
Published:	New York, NY [u.a.] McGraw-Hill [u.a.] 1974
Edition:	Third edition, International Student Edition
Subjects:	Complexe variabelen Functies (wiskunde) Functions of complex variables Funktionentheorie Funktion > Mathematik Mehrere komplexe Variable
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001264339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	1. Auflage unter dem Titel: Churchill, Ruel V.: Introduction to complex variables and applications
Physical Description:	X, 332 Seiten graph. Darst.
ISBN:	0070108552

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Record in the Search Index

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adam_text	CONTENTS Preface ix 1. Complex Numbers 1 Definition. Algebraic Properties. Cartesian Coordinates. The Triangle Inequality. Polar Coordinates. Powers and Roots. Regions in the Complex Plane. The Point at Infinity. 2. Analytic Functions 22 Functions of a Complex Variable. Mappings. Limits. Theorems on Limits. Continuity. Derivatives. Differentiation Formulas. The Cauchy- Riemann Equations. Sufficient Conditions. The Cauchy-Riemann Equa¬ tions in Polar Form. Analytic Functions. Harmonic Functions. 3. Elementary Functions 52 The Exponential Function. Other Properties of exp z. Trigonometric Functions. Further Properties of Trigonometric Functions. Hyperbolic Functions. The Logarithmic Function. Branches of log z. Further Prop¬ erties of Logarithms. Complex Exponents. Inverse Trigonometric Functions. VI CONTENTS 4. Mapping by Elementary Functions 72 Linear Functions. The Function 1/z. Linear Fractional Transformations. Special Linear Fractional Transformations. The Function r . The Func¬ tion z1 2. Other Irrational Functions. The Transformation w = exp z. The Transformation w = sin z. Successive Transformations. Table of Transformations of Regions. 5. Integrals 102 Definite Integrals. Contours. Line Integrals. Examples. The Cauchy- Goursat Theorem. A Preliminary Lemma. Proof of the Cauchy-Goursat Theorem. Simply and Multiply Connected Domains. Indefinite Integrals. The Cauchy Integral Formula. Derivatives of Analytic Functions. Morera s Theorem. Maximum Moduli of Functions. The Fundamental Theorem of Algebra. 6. Series 141 Convergence of Sequences and Series. Taylor Series. Observations and Examples. Laurent Series. Further Properties of Series. Uniform Con¬ vergence. Integration and Differentiation of Power Series. Uniqueness of Representations. Multiplication and Division. Examples. Zeros of Analytic Functions. 7. Residues and Poles 170 Residues. The Residue Theorem. The Principal Part of a Function. Poles. Quotients of Analytic Functions. Evaluation of Improper Real Integrals. Improper Integrals Involving Trigonometric Functions. Definite Integrals of Trigonometric Functions. Integration Around a Branch Point. 8. Conformal Mapping 195 Basic Properties. Further Properties and Examples. Harmonic Conjugates. Transformations of Harmonic Functions. Transformations of Boundary Conditions. 9. Applications of Conformal Mapping 209 Steady Temperatures. Steady Temperatures in a Half Plane. A Related Problem. Temperatures in a Quadrant with Part of One Boundary Insulat¬ ed. Electrostatic Potential. Potential in a Cylindrical Space. Two-dimen¬ sional Fluid Flow. The Stream Function. Flow around a Corner. Flow around a Cylinder. CONTENTS VU 10. The Schwarz-Christoffel Transformation 239 Mapping the Real Axis onto a Polygon. The Schwarz-Christoffel Trans¬ formation. Triangles and Rectangles. Degenerate Polygons. The Infinite Strip. Fluid Flow in a Channel through a Slit. Flow in a Channel with an Offset. Electrostatic Potential about an Edge of a Conducting Plate. 11. Integral Formulas of Poisson Type 264 The Poisson Integral Formula. A Dirichlet Problem for a Disk. Related Boundary Value Problems. Integral Formulas for a Half Plane. A Dirichlet Problem for a Half Plane. A Neumann Problem for a Disk. A Neumann Problem for a Half Plane. 12. Further Theory of Functions 283 A. Analytic Continuation 283 Conditions under which /(z) = 0. Permanence of Forms of Functional Identities. Uniqueness of Analytic Continuation. Examples. The Principal of Reflection. B. Singular Points and Zeros 293 Poles and Zeros. Essential Singular Points. The Number of Zeros and Poles. The Argument Principle. C. Riemann Surfaces 303 A Surface for log z. A Surface for z1/2. Surfaces for other Irrational Func¬ tions. Appendixes 1. Bibliography 311 2. Table of Transformations of Regions 315 Index 425
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isbn	0070108552
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spellingShingle	Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- Verhey, Roger F. Complex variables and applications Complexe variabelen gtt Functies (wiskunde) gtt Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd
subject_GND	(DE-588)4018935-1 (DE-588)4071510-3 (DE-588)4169285-8
title	Complex variables and applications
title_auth	Complex variables and applications
title_exact_search	Complex variables and applications
title_full	Complex variables and applications Ruel V. Churchill, Professor Emeritus of Mathematics, University of Michigan, James W. Brown, Professor of Mathematics, University of Michigan - Dearborn, Roger F. Verhey, Professor of Mathematics, University of Michigan - Dearborn
title_fullStr	Complex variables and applications Ruel V. Churchill, Professor Emeritus of Mathematics, University of Michigan, James W. Brown, Professor of Mathematics, University of Michigan - Dearborn, Roger F. Verhey, Professor of Mathematics, University of Michigan - Dearborn
title_full_unstemmed	Complex variables and applications Ruel V. Churchill, Professor Emeritus of Mathematics, University of Michigan, James W. Brown, Professor of Mathematics, University of Michigan - Dearborn, Roger F. Verhey, Professor of Mathematics, University of Michigan - Dearborn
title_old	Churchill Introduction to complex varaibles and applications
title_short	Complex variables and applications
title_sort	complex variables and applications
topic	Complexe variabelen gtt Functies (wiskunde) gtt Functions of complex variables Funktionentheorie (DE-588)4018935-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd
topic_facet	Complexe variabelen Functies (wiskunde) Functions of complex variables Funktionentheorie Funktion Mathematik Mehrere komplexe Variable
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001264339&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT churchillruelvance complexvariablesandapplications AT brownjamesward complexvariablesandapplications AT verheyrogerf complexvariablesandapplications

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