Complex variables and applications:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Tokyo [u.a.]
McGraw-Hill Kogakusha
1974
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | International Student edition |
| Physical Description: | 332 S. |
| ISBN: | 0070854157 |
Staff View
MARC
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| 245 | 1 | 0 | |a Complex variables and applications |c Ruel V. Churchill ; James W. Brown ; Roger F. Verhey |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Tokyo [u.a.] |b McGraw-Hill Kogakusha |c 1974 | |
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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
|
| adam_txt |
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 |
| any_adam_object | 1 |
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| discipline_str_mv | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:03:35Z |
| indexdate | 2024-07-09T20:46:30Z |
| institution | BVB |
| isbn | 0070854157 |
| language | English |
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| physical | 332 S. |
| publishDate | 1974 |
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| publisher | McGraw-Hill Kogakusha |
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| spelling | Churchill, Ruel Vance 1899-1987 Verfasser (DE-588)115367608 aut Complex variables and applications Ruel V. Churchill ; James W. Brown ; Roger F. Verhey 3. ed. Tokyo [u.a.] McGraw-Hill Kogakusha 1974 332 S. txt rdacontent n rdamedia nc rdacarrier International Student edition Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 s DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s Funktionentheorie (DE-588)4018935-1 s 1\p DE-604 Brown, James Ward 1934- Verfasser (DE-588)136655386 aut Verhey, Roger F. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015091590&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 |
| spellingShingle | Churchill, Ruel Vance 1899-1987 Brown, James Ward 1934- Verhey, Roger F. Complex variables and applications 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_exact_search_txtP | Complex variables and applications |
| title_full | Complex variables and applications Ruel V. Churchill ; James W. Brown ; Roger F. Verhey |
| title_fullStr | Complex variables and applications Ruel V. Churchill ; James W. Brown ; Roger F. Verhey |
| title_full_unstemmed | Complex variables and applications Ruel V. Churchill ; James W. Brown ; Roger F. Verhey |
| title_short | Complex variables and applications |
| title_sort | complex variables and applications |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Funktionentheorie Funktion Mathematik Mehrere komplexe Variable |
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