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1An Introduction To The Theory Of Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.509804 dc.contributor.author: Copson E.t dc.date.accessioned: 2015-09-29T15:14:58Z dc.date.available: 2015-09-29T15:14:58Z dc.date.copyright: 1935 dc.date.digitalpublicationdate: 2012 dc.date.citation: 1935 dc.identifier.other: 136727 dc.identifier.barcode: 99999990855366 dc.identifier.origpath: /data55/upload/0057/083 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/509804 dc.description.scannerno: 2 dc.description.scanningcentre: Allama Iqbal Library, University of Kashmir 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: Delhi, Oxford University Press,bombay,calcutta And Madras dc.rights: In Public Domain dc.source.library: Allam Iqbal Library Kashmir University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.title: An Introduction To The Theory Of Functions Of A Complex Variable dc.type: Print - Paper dc.type: Book

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2Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.509804 dc.contributor.author: Copson E.t dc.date.accessioned: 2015-09-29T15:14:58Z dc.date.available: 2015-09-29T15:14:58Z dc.date.copyright: 1935 dc.date.digitalpublicationdate: 2012 dc.date.citation: 1935 dc.identifier.other: 136727 dc.identifier.barcode: 99999990855366 dc.identifier.origpath: /data55/upload/0057/083 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/509804 dc.description.scannerno: 2 dc.description.scanningcentre: Allama Iqbal Library, University of Kashmir 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: Delhi, Oxford University Press,bombay,calcutta And Madras dc.rights: In Public Domain dc.source.library: Allam Iqbal Library Kashmir University dc.subject.classification: Natural Sciences dc.subject.classification: Mathematics dc.title: An Introduction To The Theory Of Functions Of A Complex Variable dc.type: Print - Paper dc.type: Book

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3An Intoduction To The Theory Of Functions Of A Complex Variable

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Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 6/24/2015 2:01 The Digital Library of India was a project under the auspices of the Government of India.

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4Complex Functions;: A First Course In The Theory Of Functions Of A Single Complex Variable

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Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 6/24/2015 2:01 The Digital Library of India was a project under the auspices of the Government of India.

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5Theory Of Functions Of A Complex Variable

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Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Ratan Tata Library, University Delhi Date Accessioned: 6/19/2015 17:32 The Digital Library of India was a project under the auspices of the Government of India.

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6Theory Of Functions Of A Complex Variable

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xxii, 682 p. 28 cm

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7Functions Of A Complex Variable- Lecture 12- The Local Mapping. Schwarz's Lemma And Non-Euclidean Interpretation.

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Non-Euclidean Plane: This is the unit disk |z| < 1 with the following convention: a) Non-Euclidean point = Point in disk; b) Non-Euclidean line = Arc in disk perpendicular to the boundary

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8Space And Geometry Irrational Numbers And Their Representation By Sequences And Series Auslese Aus Meiner Unterrichts- Und Vorlesungspraxis Leçons De Géométrie Supérieure La Géométrie Analytique Génerale N H Abel: Sa Vie Et Son Uvre Theory Of The Algebraic Functions Of A Complex Variable Recherches Sur L'Élasticité

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“Space And Geometry Irrational Numbers And Their Representation By Sequences And Series Auslese Aus Meiner Unterrichts- Und Vorlesungspraxis Leçons De Géométrie Supérieure La Géométrie Analytique Génerale N H Abel: Sa Vie Et Son Uvre Theory Of The Algebraic Functions Of A Complex Variable Recherches Sur L'Élasticité” Metadata:

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9Elements Of The Theory Of Functions Of A Complex Variable

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10Functions Of A Complex Variable (2016) By Kausukhkh Virathavara

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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11Functions Of A Complex Variable- Lecture 2- Exponential Function & Logarithm For A Complex Argument

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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12Functions Of A Complex Variable- Lecture 4- Power Series

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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13Functions Of A Complex Variable Being Part I Of Volume I

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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14Applied Functions Of A Complex Variable

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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15GRAPHICAL REPRESENTATION OF SOME OF THE SIMPLER ANALYTIC FUNCTIONS OF A COMPLEX VARIABLE

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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16The Taylor Series; An Introduction To The Theory Of Functions Of A Complex Variable

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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17Theory Of Functions Of A Complex Variable

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Exercises from Functions of a Complex Variable, Virathavara (2016), answered as part if bible study for a pilgrimage.

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18Theory Of Functions Of A Complex Variable Vol. I, II

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Classical reference on Theory of functions of complex variable

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19Selected Topics In The Classical Theory Of Functions Of A Complex Variable

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20Functions Of A Complex Variable

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Classical reference on Theory of functions of complex variable

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21The Functions Of A Complex Variable Defined By An Ordinary Differential Equation Of The First Order And The First Degree

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"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

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22Theory Of Functions Of A Complex Variable

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"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

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23An Introduction To The Theory Of Functions Of A Complex Variable

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"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

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24Functions Of A Complex Variable

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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

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25Mathematical Analysis Volume-1i(functions Of A Complex Variable

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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

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26Functions Of A Complex Variable

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

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27An Introduction To The Theory Of Functions Of A Complex Variable

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448 p. ; 23 cm

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28A Table And Method Of Computation Of Electric Wave Propagation, Transmission Line Phenomena, Optical Refraction, And Inverse Hyperbolic Functions Of A Complex Variable

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"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

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29Theory Of Functions Of A Complex Variable

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"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

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30Theory Of Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.153706 dc.contributor.author: A. R. Forsyth dc.date.accessioned: 2015-07-06T19:21:34Z dc.date.available: 2015-07-06T19:21:34Z dc.date.digitalpublicationdate: 2004-06-29 dc.date.citation: 1918 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2999990018958 dc.identifier.origpath: /data/upload/0018/963 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/153706 dc.description.numberedpages: 885 dc.description.numberedpages: 37 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 922 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Cambridge University Press dc.rights: Public Domain dc.title: Theory Of Functions Of A Complex Variable

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31Elements_of_the_Theory_of_Functions_of_a_Complex_Variable

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Book Source: Digital Library of India Item 2015.153706 dc.contributor.author: A. R. Forsyth dc.date.accessioned: 2015-07-06T19:21:34Z dc.date.available: 2015-07-06T19:21:34Z dc.date.digitalpublicationdate: 2004-06-29 dc.date.citation: 1918 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2999990018958 dc.identifier.origpath: /data/upload/0018/963 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/153706 dc.description.numberedpages: 885 dc.description.numberedpages: 37 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 922 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Cambridge University Press dc.rights: Public Domain dc.title: Theory Of Functions Of A Complex Variable

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32Functions Of A Complex Variable, With Applications. Second Edition.

Book Source: Digital Library of India Item 2015.153706 dc.contributor.author: A. R. Forsyth dc.date.accessioned: 2015-07-06T19:21:34Z dc.date.available: 2015-07-06T19:21:34Z dc.date.digitalpublicationdate: 2004-06-29 dc.date.citation: 1918 dc.identifier: RMSC, IIIT-H dc.identifier.barcode: 2999990018958 dc.identifier.origpath: /data/upload/0018/963 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/153706 dc.description.numberedpages: 885 dc.description.numberedpages: 37 dc.description.scanningcentre: RMSC, IIIT-H dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 922 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Universal Digital Library dc.publisher: Cambridge University Press dc.rights: Public Domain dc.title: Theory Of Functions Of A Complex Variable

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33Functions Of A Complex Variable With Applications

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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.

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34Functions Of A Complex Variable

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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.

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35An Introduction To The Theory Of Functions Of A Complex Variable

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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.

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36Analytic Functions Of A Complex Variable

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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.

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37Theory Of Functions Of A Complex Variable

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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.

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38Theory Of Functions Of A Complex Variable; Authorized Translation From The 4th German Ed., With The Addition Of Figures And Exercises.

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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.

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39Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.212410 dc.contributor.other: Hedrick, Earle Raymond dc.date.accessioned: 2015-07-09T17:58:30Z dc.date.available: 2015-07-09T17:58:30Z dc.date.digitalpublicationdate: 2004-01-05 dc.date.citation: 1916 dc.identifier.barcode: 99999990081881 dc.identifier.origpath: /data_copy/upload/0081/886 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/212410 dc.description.scanningcentre: IIAp, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 291 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Dover Publications Inc, New York dc.rights: In Public Domain dc.source.library: Indian Institute Of Astrophysics dc.title: Functions Of A Complex Variable

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40Elements Of The Theory Of Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.164336 dc.contributor.author: Dr.h.durege dc.contributor.other: Carnegie Mellon University dc.date.accessioned: 2015-07-06T23:23:55Z dc.date.available: 2015-07-06T23:23:55Z dc.date.citation: 1896 dc.identifier.barcode: 1990040033780 dc.identifier.origpath: /data/upload/0033/785 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/164336 dc.description.scanningcentre: SASTRA University, Thanjavur dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 301 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: N.srinivasan dc.publisher: G.e.fisher And I.j.schwatt,philadelphia dc.rights: Out_of_copyright dc.title: Elements Of The Theory Of Functions Of A Complex Variable

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41Theory Of Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.164336 dc.contributor.author: Dr.h.durege dc.contributor.other: Carnegie Mellon University dc.date.accessioned: 2015-07-06T23:23:55Z dc.date.available: 2015-07-06T23:23:55Z dc.date.citation: 1896 dc.identifier.barcode: 1990040033780 dc.identifier.origpath: /data/upload/0033/785 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/164336 dc.description.scanningcentre: SASTRA University, Thanjavur dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 301 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: N.srinivasan dc.publisher: G.e.fisher And I.j.schwatt,philadelphia dc.rights: Out_of_copyright dc.title: Elements Of The Theory Of Functions Of A Complex Variable

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42Note On The Functions Defined By Infinite Series Whose Terms Are Analytic Functions Of A Complex Variable; With Corresponding Theorems For Definite Integrals

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"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

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43Elements Of The Theory Of Functions Of A Complex Variable With Especial Reference To The Methods Of Riemann

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"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

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44Functions Of A Complex Variable- Lecture 16- Harmonic Functions

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While integrals like _ f(z) dz and _ M dx+ N dy have been de�ned in the text (p.101), di_erential forms like dx, dy and dz = dx + i dy have not been de�ned (and the de�nition is more subtle), we shall develop the theory of harmonic functions (p.162-170) without di_erential forms.

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45The Theory Of Functions Of A Complex Variable

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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

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46Functions Of A Complex Variable- Lecture 1- The Algebra Of Complex Numbers

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we show that the spherical representation z _ Z is conformal. This means that if l and m are two lines in the plane intersecting in z at an angle _, then the corresponding circles C and D through N and Z intersect Z at the same angle _

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47Functions Of A Complex Variable- Lecture 11- Isolated Singularities

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Theorem 9: A holomorphic function comes arbitrarily close to any complex value in every neighborhood of an essential singularity.

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48Functions Of A Complex Variable- Lecture 19- Normal Families

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Theorem 1 Let � _ C be a region, F a family of holomorphic functions on � such that for each compact E _ �, F is uniformly bounded on E. Then F has a subsequence converging uniformly on each compact subset of �.

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49Functions Of A Complex Variable

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Book Source: Digital Library of India Item 2015.448900 dc.contributor.author: Jain R, N, dc.date.accessioned: 2015-09-18T18:23:55Z dc.date.available: 2015-09-18T18:23:55Z dc.date.digitalpublicationdate: 2015 dc.identifier.other: 8368 dc.identifier.barcode: 99999990907439 dc.identifier.origpath: /data58/upload/0109/156 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/448900 dc.description.scannerno: 6 dc.description.scanningcentre: Allama Iqbal Library, University of Kashmir dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 210 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Lakshmi Narain Agarwal Agra dc.rights: Not Available dc.source.library: Womens College, M. A Road Srinagar dc.subject.classification: Natural Sciences dc.title: Functions Of A Complex Variable dc.type: Print - Paper dc.type: Book

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50Functions Of A Complex Variable Vol Ii

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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

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