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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.

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.

"A Table and Method of Computation of Electric Wave Propagation, Transmission Line Phenomena, Optical Refraction, and Inverse Hyperbolic Functions of a Complex Variable" is an article from Proceedings of the American Academy of Arts and Sciences, Volume 57 . View more articles from Proceedings of the American Academy of Arts and Sciences . 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-20025901

viii, 218 p. illus. ; 23 cm

448 p. ; 23 cm

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

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

"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

"The Functions of a Complex Variable Defined by an Ordinary Differential Equation of the First Order and the First Degree" is an article from Transactions of the American Mathematical Society, Volume 16 . 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-1988747

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.

Book Source: Digital Library of India Item 2015.164384 dc.contributor.author: Edouard Goursat, Earle Raymond Hedrick, Otto Dunkel dc.contributor.other: Carnegie Library dc.date.accessioned: 2015-07-06T23:25:03Z dc.date.available: 2015-07-06T23:25:03Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1916 dc.identifier.barcode: 1990040033824 dc.identifier.origpath: /data/upload/0033/829 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/164384 dc.description.scanningcentre: SASTRA University, Thanjavur dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 270 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: V.krishnamoorthy dc.publisher: Ginn And Company dc.rights: Out_of_copyright dc.subject.classification: Mathematics dc.title: Mathematical Analysis Volume-1i(functions Of A Complex Variable

Book Source: Digital Library of India Item 2015.153591 dc.contributor.author: E. J. Townsend dc.date.accessioned: 2015-07-06T19:19:14Z dc.date.available: 2015-07-06T19:19:14Z dc.date.digitalpublicationdate: 2004-06-28 dc.date.citation: 1915 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2999990018854 dc.identifier.origpath: /data/upload/0018/859 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/153591 dc.description.numberedpages: 384 dc.description.numberedpages: 20 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 404 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Henry Holt And Company dc.rights: Public Domain dc.title: Functions Of A Complex Variable dc.rights.holder: Henry Holt And Company

Book Source: Digital Library of India Item 2015.84442 dc.contributor.author: Morse,marston. dc.date.accessioned: 2015-06-30T18:51:37Z dc.date.available: 2015-06-30T18:51:37Z dc.date.digitalpublicationdate: 2005-03-29 dc.date.citation: 1947 dc.identifier.barcode: 2030020000917 dc.identifier.origpath: /data7/upload/0168/938 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/84442 dc.description.scannerno: 1 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 160 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Princeton University Press dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Number Theory dc.title: Topological Methods In The Theory Of Functions Of A Complex Variable

Book Source: Digital Library of India Item 2015.84442 dc.contributor.author: Morse,marston. dc.date.accessioned: 2015-06-30T18:51:37Z dc.date.available: 2015-06-30T18:51:37Z dc.date.digitalpublicationdate: 2005-03-29 dc.date.citation: 1947 dc.identifier.barcode: 2030020000917 dc.identifier.origpath: /data7/upload/0168/938 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/84442 dc.description.scannerno: 1 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 160 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Princeton University Press dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Number Theory dc.title: Topological Methods In The Theory Of Functions Of A Complex Variable

Book Source: Digital Library of India Item 2015.84442 dc.contributor.author: Morse,marston. dc.date.accessioned: 2015-06-30T18:51:37Z dc.date.available: 2015-06-30T18:51:37Z dc.date.digitalpublicationdate: 2005-03-29 dc.date.citation: 1947 dc.identifier.barcode: 2030020000917 dc.identifier.origpath: /data7/upload/0168/938 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/84442 dc.description.scannerno: 1 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 160 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Princeton University Press dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Number Theory dc.title: Topological Methods In The Theory Of Functions Of A Complex Variable

"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

Book Source: Digital Library of India Item 2015.233836 dc.contributor.author: Copson E.t. dc.date.accessioned: 2015-07-10T18:57:27Z dc.date.available: 2015-07-10T18:57:27Z dc.date.digitalpublicationdate: 2005-12-29 dc.date.citation: 1935 dc.identifier.barcode: 99999990131171 dc.identifier.origpath: /rawdataupload1/upload/0129/833 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/233836 dc.description.scanningcentre: C-DAC, Noida dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 460 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: The Clarendon Press, Oxford dc.rights: Not Available dc.source.library: Ratan Tata Library, University Delhi dc.subject.classification: Natural Sciences dc.subject.keywords: Variables dc.subject.keywords: Theorem dc.title: Theory Of Functions Of A Complex Variable

Book Source: Digital Library of India Item 2015.233836 dc.contributor.author: Copson E.t. dc.date.accessioned: 2015-07-10T18:57:27Z dc.date.available: 2015-07-10T18:57:27Z dc.date.digitalpublicationdate: 2005-12-29 dc.date.citation: 1935 dc.identifier.barcode: 99999990131171 dc.identifier.origpath: /rawdataupload1/upload/0129/833 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/233836 dc.description.scanningcentre: C-DAC, Noida dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 460 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: The Clarendon Press, Oxford dc.rights: Not Available dc.source.library: Ratan Tata Library, University Delhi dc.subject.classification: Natural Sciences dc.subject.keywords: Variables dc.subject.keywords: Theorem dc.title: Theory Of Functions Of A Complex Variable

Book Source: Digital Library of India Item 2015.233836 dc.contributor.author: Copson E.t. dc.date.accessioned: 2015-07-10T18:57:27Z dc.date.available: 2015-07-10T18:57:27Z dc.date.digitalpublicationdate: 2005-12-29 dc.date.citation: 1935 dc.identifier.barcode: 99999990131171 dc.identifier.origpath: /rawdataupload1/upload/0129/833 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/233836 dc.description.scanningcentre: C-DAC, Noida dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 460 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: The Clarendon Press, Oxford dc.rights: Not Available dc.source.library: Ratan Tata Library, University Delhi dc.subject.classification: Natural Sciences dc.subject.keywords: Variables dc.subject.keywords: Theorem dc.title: Theory Of Functions Of A Complex Variable

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

xiii, 432 p. 21 cm

xiii, 432 p. 21 cm

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

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

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

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

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

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

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

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

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

The modern engineer often has to do with problems that require a sound mathematical background and set skills in the use of diverse mathematical methods. Expanding the mathematical outlook of the engineer contributes appreciably to new advances in technology. The theory of functions of a complex variable, operational calculus, and stability theory are most important for applications. The present text is designed for students of engineering colleges and also for practicing engineers who feel a need to refresh their knowledge of such important areas of mathematics. Each section of the text starts out with a brief review of the essentials of theory (propositions, definitions, formulas). This is followed by examples with detailed solutions and exercises. The book contains about 1000 examples and problems to be solved by the student. Translated from the Russian by Eugene Yankovsky All credits to IA user Quantum AI . Contents Chapter 1. Functions of a Complex Variable § 1. Complex Numbers and Operations with Them § 2. Functions of a Complex Variable § 3. The Limit of a Sequence of Complex Numbers. The Limit and Continuity of a Function of a Complex Variable § 4. Differentiating Functions of a Complex Variable. The Cauchy–Riemann Conditions § 5. Integrating Functions of a Complex Variable § 6. Cauchy’s Integral Formula § 7. Series in the Complex Domain § 8. Zeros of a Function. Isolated Singularities § 9. Residues of a Function § 10. The Residue Theorem. Applying Residues to Evaluate Definite Integrals. Summation of Series by Means of Residues § 11. The Logarithmic Residue. The Argument Principle. Rouche’s Theorem § 12. Conformal Mapping § 13. The Complex-Valued Potential and Its Hydrodynamic Interpretation Chapter 2. Operational Calculus § 14. Finding Object and Result Functions § 15. Solving the Cauchy Problem for Linear Ordinary Differential Equations with Constant Coefficients § 16. Duhamel’s Integral § 17. Solving Systems of Linear Differential Equations by the Operational Method § 18. Solving Volterra’s Integral Equations with Kernels of a Special Type § 19. Differential Equations with Retarded Arguments § 20. Solving Some Problems of Mathematical Physics § 21. Discrete Laplace Transformation Chapter 3. Stability Theory § 22. Stability of Solutions of Systems of Differential Equations. The Simplest Types of Equilibrium Solutions § 23. Lyapunov’s Second Method § 24. Stability in the First Approximation § 25. Asymptotic Stability in the Large. Lagrange Stability § 26. The Routh–Hurwitz Criterion § 27. Geometric Criterion of Stability (Mikhailov’s Criterion) § 28. Regions of Stability § 29. Stability of Solutions of Difference Equations Answers Appendix: Object and Result Functions Selected Bibliography

"A Graphical Aid in the Study of Functions of a Complex Variable" is an article from The American Mathematical Monthly, Volume 27 . View more articles from The American Mathematical Monthly . 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-2972550

"A Graphical Aid in the Study of Functions of a Complex Variable" is an article from The American Mathematical Monthly, Volume 27 . View more articles from The American Mathematical Monthly . 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-2972550

"A Graphical Aid in the Study of Functions of a Complex Variable" is an article from The American Mathematical Monthly, Volume 27 . View more articles from The American Mathematical Monthly . 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-2972550

xxiv, 855, [1] p. 27 cm

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)

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)

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)

Book Source: Digital Library of India Item 2015.205782 dc.contributor.author: Goursat,edouard. dc.date.accessioned: 2015-07-09T14:17:33Z dc.date.available: 2015-07-09T14:17:33Z dc.date.digitalpublicationdate: 2005-05-31 dc.date.citation: 1916 dc.identifier.barcode: 2990140054501 dc.identifier.origpath: /data_copy/upload/0054/506 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/205782 dc.description.scannerno: 3 dc.description.scanningcentre: Osmania University dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 280 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Ginn And Company. dc.rights: Copyright Permitted dc.source.library: Osmania University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.subject.classification: Fundamental And General Consideration Of Mathematics dc.title: Functions Of A Complex Variable Vol Ii