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"Line-Geometric Representations for Functions of a Complex Variable" is an article from Transactions of the American Mathematical Society, Volume 20 . View more articles from Transactions of the American Mathematical Society . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-1988802

"Line-Geometric Representations for Functions of a Complex Variable" is an article from Transactions of the American Mathematical Society, Volume 20 . View more articles from Transactions of the American Mathematical Society . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-1988802

Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

About the book The book covers basic aspects of complex numbers, complex variables and complex functions. It also deals with analytic functions, Laurent series etc. Contents Introduction 9 Chapter 1. THE COMPLEX VARIABLE AND FUNCTIONS OF A COMPLEX VARIABLE 11 1.1. Complex Numbers and Operations on Complex Numbers 11 a. The concept of a complex number 11 b. Operations on complex numbers 11 c. The geometric interpretation of complex numbers 13 d. Extracting the root of a complex number 15 1.2. The Limit of a Sequence of Complex Numbers 17 a. The definition of a convergent sequence 17 b. Cauchy's test 19 c. Point at infinity 19 1.3. The Concept of a Function of a Complex Variable. Continuity 20 a. Basic definitions 20 b. Continuity 23 c. Examples 26 1.4. Differentiating the Function of a Complex Variable 30 a. Definition. Cauchy-Riemann conditions 30 b. Properties of analytic functions 33 c. The geometric meaning of the derivative of a function of a complex variable 35 d. Examples 37 1.5. An Integral with Respect to a Complex Variable 38 a. Basic properties 38 b. Cauchy's Theorem 41 c. Indefinite Integral 44 1.6. Cauchy's Integral 47 a. Deriving Cauchy's formula 47 b. Corollaries to Cauchy's formula 50 c. The maximum-modulus principle of an analytic function 51 1.7. Integrals Dependent on a Parameter 53 a. Analytic dependence on a parameter 53 b. An analytic function and the existence of derivatives of all orders 55 Chapter 2. SERIES OF ANALYTIC FUNCTIONS 58 2.1. Uniformly Convergent Series of Functions of a Complex Variable 58 a. Number series 58 b. Functional series. Uniform convergence 59 c. Properties of uniformly convergent series. Weierstrass' theorems 62 d. Improper integrals dependent on a parameter 66 2.2. Power Series. Taylor's Series 67 a. Abel's theorem 67 b. Taylor's series 72 c. Examples 74 2.3. Uniqueness of Definition of an Analytic Function 76 a. Zeros of an analytic function 76 b. Uniqueness theorem 77 Chapter 3. ANALYTIC CONTINUATION. ELEMENTARY FUNCTIONS OF A COMPLEX VARIABLE 80 3.1. Elementary Functions of a Complex Variable. Continuation from the Real Axis 80 a. Continuation from the real axis 80 b. Continuation of relations 84 c. Properties of elementary functions 87 d. Mappings of elementary functions 91 3.2. Analytic Continuation. The Riemann Surface 95 a. Basic principles. The concept of a Riemann surface 95 b. Analytic continuation across a boundary 98 c. Examples in constructing analytic continuations. Continuation across a boundary 100 d. Examples in constructing analytic continuations. Continuation by means of power series 105 e. Regular and singular points of an analytic function 108 f. The concept of a complete analytic function 111 Chapter 4. THE LAURENT SERIES AND ISOLATED SINGULAR POINTS 113 4.1. The Laurent Series 113 a. The domain of convergence of a Laurent series 113 b. Expansion of an analytic function in a Laurent series 115 4.2. A Classification of the Isolated Singular Points of a Single-Valued Analytic Function 118 Chapter 5. RESIDUES AND THEIR APPLICATIONS 125 5.1. The Residue of an Analytic Function at an Isolated Singularity 125 a. Definition of a residue. Formulas for evaluating residues 125 b. The residue theorem 127 5.2. Evaluation of Definite Integrals by !\leans of Residues 130 a. Integrals of the form $\int^{2 \pi}_{0}R (\cos \theta \sin \theta ) d \theta$ 131 b. Integrals of the form $\int^{\infty}_{\infty} f(x)dx$ 132 c. Integrals of the form $\int^{\infty}_{\infty} \exp(iax)f(x)dx$. Jordan's lemma  135 d. The case of multiple-valued functions 141 5.3. Logarithmic Residue 147 a. The concept of a logarithmic residue 147 b. Counting the number of zeros of an analytic function 149 Chapter 6. CONFORMAL MAPPING 153 6.1. General Properties 153 a. Definition of a conformal mapping 153 b. Elementary examples 157 c. Basic principles 160 d. Riemann's theorem 166 6.2. Linear-Fractional Function 169 6.3. Zhukovsky's Function 179 6.4. Schwartz-Christoffel Integral. Transformation of Polygons 181 Chapter 7. ANALYTIC FUNCTIONS IN THE SOLUTION OF BOUNDARY-VALUE PROBLEMS 191 7. 1. Generalities 191 a. The relationship of analytic and harmonic functions 191 b. Preservation of the Laplace operator in a conformal mapping 192 c. Dirichlet's problem 194 d. Constructing a source function 197 7.2. Applications to Problems in Mechanics and Physics 199 a. Two-dimensional steady-state flow of a fluid 199 b. A two-dimensional electrostatic field 211 Chapter 8. FUNDAMENTALS OF OPERATIONAL CALCULUS 221 8.1. Basic Properties of the Laplace Transformation 221 a. Definition 221 b. Transforms of elementary functions 225 c. Properties of a transform 227 d. Table of properties of transforms 236 e. Table of transforms 236 8.2. Determining the Original Function from the Transform 238 a. Mellin's formula 238 h. Existence conditions of the original function 241 c. Computing the Mellin integral 245 d. The case of a function regular at infinity 249 8.3. Solving Problems for Linear Differential Equations by the Operational Method 252 a. Ordinary differential equations 252 b. Heat-conduction equation 257 c. The boundary-value problem for a partial differential equation 259 Appendix I. SADDLE-POINT METHOD 261 I.1. Introductory Remarks 261 I.2. Laplace's Method 264 I.3. The Saddle-Point Method 271 Appendix II. THE WIENER-HOPF METHOD 280 II.1. Introductory Remarks 280 11.2. Analytic Properties of the Fourier Transformation 284 11.3. Integral Equations with a Difference Kernel 287 II.4. General Scheme of the Wiener-Hopf Method 292 II.5. Problems Which Reduce to Integral Equations with a Difference Kernel 297 a. Derivation of Milne's equation 297 b. Investigating the solution of Milne's equation 301 c. Diffraction on a flat screen 305 II.6. Solving Boundary-Value Problems for Partial Differential Equations by the Wiener-Hopf Method 306 Appendix III. FUNCTIONS OF MANY COMPLEX VARIABLES 310 III.1. Basic Definitions 310 III.2. The Concept of an Analytic Function of Many Complex Variables 311 III.3. Cauchy's Formula 312 III.4. Power Series 314 III.5. Taylor's Series 316 III.6. Analytic Continuation 317 Appendix IV. WATSON'S METHOD 320 References 328 Name Index 329 Subject Index 330

viii, 218 p. illus. ; 23 cm

viii, 218 p. illus. ; 23 cm

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Book Source: Digital Library of India Item 2015.240890 dc.contributor.author: Goursat Edouard dc.date.accessioned: 2015-07-14T19:31:22Z dc.date.available: 2015-07-14T19:31:22Z dc.date.copyright: 1916 dc.date.digitalpublicationdate: 2014 dc.date.citation: 1916 dc.identifier.other: 4196 dc.identifier.barcode: 99999990881449 dc.identifier.origpath: /data58/upload/0083/166 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/240890 dc.description.scannerno: 2 dc.description.scanningcentre: Allama Iqbal Library, University of Kashmir dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 272 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Ginn And Company, London dc.rights: In Public Domain dc.source.library: Women College M.A Road Srinagar dc.subject.classification: Natural Sciences dc.title: Functions Of A Complex Variable Part I Vol Ii dc.type: Print - Paper dc.type: Book

http://classify.oclc.org/classify2/ClassifyDemo?owi=1537043 https://www.worldcat.org/title/263098648 OCR'd with ABYY Finereader (not proofread because it's full of math), with table of contents. The original book doesn't have a cover, so I made one with a template I found online. The book is slightly wider than my scanner when fully opened, so it's not a beautiful scan, but it's readable. Title: Lectures on the Theory of Functions of a Complex Variable, Vol. 1: Holomorphic Functions Author(s): Giovanni Sansone, Johan Gerretsen Edition: 1 Series: Lectures on the Theory of Functions of a Complex Variable 1 Language: English Year: 1960 Publisher: P. Noordhoff ASIN: B0006AWCZA ( lookup at Amazon.com ) Pages: 488 (bibliographic) / 496 (file) Format: PDF File size: 86.05 Mb (90226042 bytes)

http://classify.oclc.org/classify2/ClassifyDemo?owi=1537043 https://www.worldcat.org/title/263098648 OCR'd with ABYY Finereader (not proofread because it's full of math), with table of contents. The original book doesn't have a cover, so I made one with a template I found online. The book is slightly wider than my scanner when fully opened, so it's not a beautiful scan, but it's readable. Title: Lectures on the Theory of Functions of a Complex Variable, Vol. 1: Holomorphic Functions Author(s): Giovanni Sansone, Johan Gerretsen Edition: 1 Series: Lectures on the Theory of Functions of a Complex Variable 1 Language: English Year: 1960 Publisher: P. Noordhoff ASIN: B0006AWCZA ( lookup at Amazon.com ) Pages: 488 (bibliographic) / 496 (file) Format: PDF File size: 86.05 Mb (90226042 bytes)

14

"Note on the Functions Defined by Infinite Series Whose Terms are Analytic Functions of a Complex Variable; with Corresponding Theorems for Definite Integrals" is an article from The Annals of Mathematics, Volume 3 . View more articles from The Annals of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-1967630

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Womens College, M .a Road Srinagar Date Accessioned: 8/6/2015 22:41 The Digital Library of India was a project under the auspices of the Government of India.

"On Functions Defined by an Infinite Series of Analytic Functions of a Complex Variable" is an article from The Annals of Mathematics, Volume 6 . View more articles from The Annals of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2007157

In this post we will see the book Lectures on the Theory of Functions of a Complex Variable by Yu. V. Sidorov, M. V. Fedoryuk , M. I. Shabunin. About the book This book is based on more than ten years experience in teaching the theory of functions of a complex variable at the Moscow Physics and Technology Institute. It is a textbook for students of universities and institutes of technology with an advanced mathematical program. We believe that it can also be used for independent study. We have stressed the methods of the theory that are often used in applied sciences. These methods include series expansions, conformal mapping, application of the theory of residues to evaluating definite integrals, and asymptotic methods. The material is structured in a way that will give the reader the maximum assistance in mastering the basics of the theory. To this end we have provided a wide range of worked-out examples. We hope that these will help the reader acquire a deeper understanding of the theory and experience in problem solving. The book was translated from Russian by Eugene Yankovsky and was first published by Mir in 1985. Contents Preface 5 Chapter I Introduction 9 1 Complex Numbers 9 2 Sequences and Series of Complex Numbers 20 3 Curves and Domains in the Complex Plane 25 4 Continuous Functions of a Complex Variable 36 5 Integrating Functions of a Complex Variable 45 6 The Function arg z 51 Chapter II Regular Functions 59 7 Differentiable Functions. The Cauchy-Riemann Equations 59 8 The Geometric Interpretation of the Derivative 66 9 Cauchy's Integral Theorem 76 .-- 10 Cauchy's Integral Formula 84 11 Power Series 87 12 Properties of Regular Functions 90 13 The Inverse Function 102 14 The Uniqueness Theorem 108 15 Analytic Continuation 110 16 Integrals Depending on a Parameter 112 Chapter III The Laurent Series. Isolated Singular Points of a Single-Valued Functions 123 17 The Laurent Series 123 18 Isolated Singular Points of Single- Valued Functions 128 19 Liouville's Theorem 138 Chapter IV Multiple-Valued Analytic Functions 141 20 The Concept of an Analytic Function 141 21 The Function In z 147 22 The Power Function. Branch Points of Analytic Functions 155 23 The Primitive of an Analytic Function. Inverse Trigonometric Functions 166 24 Regular Branches of Analytic Functions 170 25 Singular Boundary Points 189 26 Singular Points of Analytic Functions. The Concept of a Riemann Surface 194 27 Analytic Theory of Linear Second-Order Ordinary Differential Equations 204 Chapter V Residues and Their Applications 220 28 Residue Theorems 220 29 Use of Residues for Evaluating Definite Integrals 230 30 The Argument Principle and Rouche's Theorem 255 31 The Partial-Fraction Expansion of Meromorphic Functions 260 Chapter VI Conformal Mapping 270 32 Local Properties of Mappings Performed by Regular Functions 270 33 General Properties of Conformal Mappings 276 34 The Linear-Fractional Function 282 35 Conformal Mapping Performed by Elementary Functions 291 36 The Riemann-Schwarz Symmetry Principle 315 37 The Schwarz-Cristoffel Transformation Formula 326 38 The Dirichlet Problem 339 39 Vector Fields in a Plane 354 40 Some Physical Problems from Vector Field Theory 363 Chapter VII Simple Asymptotic Methods 371 41 Some Asymptotic Estimates 371 42 Asymptotic Expansions 389 43 Laplace's Method 396 44 The Method of Stationary Phase 409 45 The Saddle-Point Method '•18 46 Laplace's Method of Contour Integration 434 Chapter VIII Operational Calculus 446 47 Basic Properties of the Laplace Transformation 446 48 Reconstructing Object Function from Result Function 454 49 Solving Linear Differential Equations via the Laplace Transformation 468 50 String Vibrations from Instantaneous Shock 476 Selected Bibliography 486 Name Index 488 Subject Index 489

In this post we will see the book Lectures on the Theory of Functions of a Complex Variable by Yu. V. Sidorov, M. V. Fedoryuk , M. I. Shabunin. About the book This book is based on more than ten years experience in teaching the theory of functions of a complex variable at the Moscow Physics and Technology Institute. It is a textbook for students of universities and institutes of technology with an advanced mathematical program. We believe that it can also be used for independent study. We have stressed the methods of the theory that are often used in applied sciences. These methods include series expansions, conformal mapping, application of the theory of residues to evaluating definite integrals, and asymptotic methods. The material is structured in a way that will give the reader the maximum assistance in mastering the basics of the theory. To this end we have provided a wide range of worked-out examples. We hope that these will help the reader acquire a deeper understanding of the theory and experience in problem solving. The book was translated from Russian by Eugene Yankovsky and was first published by Mir in 1985. Contents Preface 5 Chapter I Introduction 9 1 Complex Numbers 9 2 Sequences and Series of Complex Numbers 20 3 Curves and Domains in the Complex Plane 25 4 Continuous Functions of a Complex Variable 36 5 Integrating Functions of a Complex Variable 45 6 The Function arg z 51 Chapter II Regular Functions 59 7 Differentiable Functions. The Cauchy-Riemann Equations 59 8 The Geometric Interpretation of the Derivative 66 9 Cauchy's Integral Theorem 76 .-- 10 Cauchy's Integral Formula 84 11 Power Series 87 12 Properties of Regular Functions 90 13 The Inverse Function 102 14 The Uniqueness Theorem 108 15 Analytic Continuation 110 16 Integrals Depending on a Parameter 112 Chapter III The Laurent Series. Isolated Singular Points of a Single-Valued Functions 123 17 The Laurent Series 123 18 Isolated Singular Points of Single- Valued Functions 128 19 Liouville's Theorem 138 Chapter IV Multiple-Valued Analytic Functions 141 20 The Concept of an Analytic Function 141 21 The Function In z 147 22 The Power Function. Branch Points of Analytic Functions 155 23 The Primitive of an Analytic Function. Inverse Trigonometric Functions 166 24 Regular Branches of Analytic Functions 170 25 Singular Boundary Points 189 26 Singular Points of Analytic Functions. The Concept of a Riemann Surface 194 27 Analytic Theory of Linear Second-Order Ordinary Differential Equations 204 Chapter V Residues and Their Applications 220 28 Residue Theorems 220 29 Use of Residues for Evaluating Definite Integrals 230 30 The Argument Principle and Rouche's Theorem 255 31 The Partial-Fraction Expansion of Meromorphic Functions 260 Chapter VI Conformal Mapping 270 32 Local Properties of Mappings Performed by Regular Functions 270 33 General Properties of Conformal Mappings 276 34 The Linear-Fractional Function 282 35 Conformal Mapping Performed by Elementary Functions 291 36 The Riemann-Schwarz Symmetry Principle 315 37 The Schwarz-Cristoffel Transformation Formula 326 38 The Dirichlet Problem 339 39 Vector Fields in a Plane 354 40 Some Physical Problems from Vector Field Theory 363 Chapter VII Simple Asymptotic Methods 371 41 Some Asymptotic Estimates 371 42 Asymptotic Expansions 389 43 Laplace's Method 396 44 The Method of Stationary Phase 409 45 The Saddle-Point Method '•18 46 Laplace's Method of Contour Integration 434 Chapter VIII Operational Calculus 446 47 Basic Properties of the Laplace Transformation 446 48 Reconstructing Object Function from Result Function 454 49 Solving Linear Differential Equations via the Laplace Transformation 468 50 String Vibrations from Instantaneous Shock 476 Selected Bibliography 486 Name Index 488 Subject Index 489

"Unabridged and unaltered republication of the third edition, published ... [in one volume] in 1918."

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Women College M.A Road Srinagar Date Accessioned: 7/14/2015 21:44 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Women College M.A Road Srinagar Date Accessioned: 7/14/2015 21:44 The Digital Library of India was a project under the auspices of the Government of India.

Here we shall give a brief proof of the general form of Cauchy�s Theorem.

The following rule (integration by substitution) is often useful.

The following rule (integration by substitution) is often useful.

The following rule (integration by substitution) is often useful.

The following rule (integration by substitution) is often useful.

vii, 384 p. 24 cm

vii, 384 p. 24 cm

vii, 384 p. 24 cm

Thesis (PH. D.)--University of Chicago, 1920

Book Source: Digital Library of India Item 2015.161973 dc.contributor.other: Indian Institute Of Science dc.date.accessioned: 2015-07-06T22:13:53Z dc.date.available: 2015-07-06T22:13:53Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1914 dc.identifier: Raman Research Institute dc.identifier.barcode: 1010010027786 dc.identifier.origpath: /data/upload/0027/791 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/161973 dc.description.scanningcentre: IISc, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 595 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Sheik dc.publisher: Ginn And Company dc.rights: United States Of America dc.source.library: Raman Research Institute dc.title: Functions Of A Complex Variable dc.rights.holder: James Pierpont

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 6/19/2015 15:56 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 6/19/2015 15:56 The Digital Library of India was a project under the auspices of the Government of India.

Book Source: Digital Library of India Item 2015.153725 dc.contributor.author: Dr. H. Durege dc.date.accessioned: 2015-07-06T19:21:57Z dc.date.available: 2015-07-06T19:21:57Z dc.date.digitalpublicationdate: 2004-06-29 dc.date.citation: 1896 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2999990018975 dc.identifier.origpath: /data/upload/0018/980 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/153725 dc.description.numberedpages: 288 dc.description.numberedpages: 20 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 308 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: G. E. Fisher And I. J. Schwatt dc.rights: Public Domain dc.title: Elements Of The Theory Of Functions Of A Complex Variable

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 6/19/2015 15:57 The Digital Library of India was a project under the auspices of the Government of India.

Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

Book digitized by Google from the library of the University of Michigan and uploaded to the Internet Archive by user tpb.

xxii, 682 p. 28 cm