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 THE present book is intended to form a supplement to Vol. I of “Functions of a Complex Variable and Some of Their Applications” by B. A. Fuchs and B.V. Shabat. It is intended for engineers, and also for students and postgraduate students of the higher technical colleges, who Wish to make themselves more familiar with some special questions in the theory of the functions of a complex variable and its applications to those chapters of mathematical analysis which play an important part in the solution of technical and physical problems (such as differential equations, the operational calculus, special functions and questions of stability).    The present book, together with the above-mentioned book by B.A. Fuchs and B.V. Shabat, will introduce the reader to the principles of the theory of the functions of a complex variable. It will acquaint him, although, of course, not exhaustively, with the special sections of this theory, which from the point of view of applications are the most important, and will give him an idea how to use its methods for the solution of applied problems. The reader is therefore assumed to have a knowledge of the foundations of complex analysis, which can be acquired from the book by B.A. Fuchs and B.V. Shabat mentioned above. Since the present book contains a large number of references to it, it Will be referred to simply as F.C.V.   For Chapters I, II and V of the present book it is sufficient to know the bases of the theory of the functions of a complex variable as set out in the version of the abbreviated study of F.C.V., which, as is stated in the Foreword to that book, gives an introduction to the elementary theory of functions. For Chaps. III and IV the second version of the abbreviated study of F.C.V., which gives the necessary introduction to operational calculus, is sufficient. The knowledge necessary can also be gained from other books containing the foundations of the general theory of the functions of a complex variable.   The book deals with the following questions: the analytic theory of differential equations (Chaps. I and II); the Laplace transformation and its applications (Chaps. III and IV) and Hurwitz’s problem for polynomials (Chap. V).   Chapter I is of a preliminary character and is devoted to algebraic functions. Principal attention is given to the study of these functions in the neighbourhoods of their regular and singular points and to their expansions into series of powers of the variable (integral and fractional, positive and negative).   Chapter II begins with a short section dealing with the analytic functions f (w, z) of two complex variables. Then differential equations of the form dw/dz = f(w, z) are considered for cases where the function f(w, z) is regular in the neighbourhood of the initial values wo, z0 of the variables w, z, where it has at w = wo, z = z0 a pole or, lastly, a point of indeterminateness. Linear differential equations of the second order are then considered, and the results obtained are applied to the Euler—Bessel equation and its integrals (cylinder functions).   Chapter III sets out the fundamental properties of the Laplace transformation and the principles of its application to the study of special functions and to the integration of differential equations. It must be emphasized that this material is treated here as a chapter on the theory of the functions of a complex variable. The authors have sought to deal simply with the most important facts on the subject, but at the same time more precisely and more strictly than is usually done in handbooks on the operational calculus for engineers. It has not been the authors’ aim to set out the actual apparatus of the operational calculus, since this can be found in many books.   Chapter IV is devoted to contour integration and asymptotic expansions. As is well known, these are of great practical value and have in general been inadequately dealt with in other books on the subject. In addition, an account is given here of the fundamental facts of the theory of asymptotic expansions, and examples of these expansions are analysed in detail. It should be noted that for the study of these questions, some knowledge is necessary of the theory of many-valued and, in particular, algebraic functions. This is to be found in the first chapter.   Chapter V treats Hurwitz’s problem for polynomials. Although it is not connected with the preceding material, the authors are agreed that its importance for a large number of applications makes its consideration essential in a book dealing with the special problems of the theory of functions of a complex variable.   In each chapter the reader will find a large number of worked examples. These are intended to serve not only as illustrations of the theoretical conclusions, but also as models for solving independently any similar problems encountered. The engineer does not usually meet the questions dealt with in this book until his problems have been already formulated mathematically. The authors have not therefore found it necessary to consider problems with marked physical content. Nevertheless, in a number of places they have emphasized the links that exist between the mathematical theories treated and the corresponding technical disciplines.   Chapters I and II were written by B. A. Fuchs, Chapters III and IV by V.I. Levin, and Chapter V by both authors together. However, the close contact constantly maintained between them during their work on the book makes them equally responsible for the volume as a whole. 

 THE present book is intended to form a supplement to Vol. I of “Functions of a Complex Variable and Some of Their Applications” by B. A. Fuchs and B.V. Shabat. It is intended for engineers, and also for students and postgraduate students of the higher technical colleges, who Wish to make themselves more familiar with some special questions in the theory of the functions of a complex variable and its applications to those chapters of mathematical analysis which play an important part in the solution of technical and physical problems (such as differential equations, the operational calculus, special functions and questions of stability).    The present book, together with the above-mentioned book by B.A. Fuchs and B.V. Shabat, will introduce the reader to the principles of the theory of the functions of a complex variable. It will acquaint him, although, of course, not exhaustively, with the special sections of this theory, which from the point of view of applications are the most important, and will give him an idea how to use its methods for the solution of applied problems. The reader is therefore assumed to have a knowledge of the foundations of complex analysis, which can be acquired from the book by B.A. Fuchs and B.V. Shabat mentioned above. Since the present book contains a large number of references to it, it Will be referred to simply as F.C.V.   For Chapters I, II and V of the present book it is sufficient to know the bases of the theory of the functions of a complex variable as set out in the version of the abbreviated study of F.C.V., which, as is stated in the Foreword to that book, gives an introduction to the elementary theory of functions. For Chaps. III and IV the second version of the abbreviated study of F.C.V., which gives the necessary introduction to operational calculus, is sufficient. The knowledge necessary can also be gained from other books containing the foundations of the general theory of the functions of a complex variable.   The book deals with the following questions: the analytic theory of differential equations (Chaps. I and II); the Laplace transformation and its applications (Chaps. III and IV) and Hurwitz’s problem for polynomials (Chap. V).   Chapter I is of a preliminary character and is devoted to algebraic functions. Principal attention is given to the study of these functions in the neighbourhoods of their regular and singular points and to their expansions into series of powers of the variable (integral and fractional, positive and negative).   Chapter II begins with a short section dealing with the analytic functions f (w, z) of two complex variables. Then differential equations of the form dw/dz = f(w, z) are considered for cases where the function f(w, z) is regular in the neighbourhood of the initial values wo, z0 of the variables w, z, where it has at w = wo, z = z0 a pole or, lastly, a point of indeterminateness. Linear differential equations of the second order are then considered, and the results obtained are applied to the Euler—Bessel equation and its integrals (cylinder functions).   Chapter III sets out the fundamental properties of the Laplace transformation and the principles of its application to the study of special functions and to the integration of differential equations. It must be emphasized that this material is treated here as a chapter on the theory of the functions of a complex variable. The authors have sought to deal simply with the most important facts on the subject, but at the same time more precisely and more strictly than is usually done in handbooks on the operational calculus for engineers. It has not been the authors’ aim to set out the actual apparatus of the operational calculus, since this can be found in many books.   Chapter IV is devoted to contour integration and asymptotic expansions. As is well known, these are of great practical value and have in general been inadequately dealt with in other books on the subject. In addition, an account is given here of the fundamental facts of the theory of asymptotic expansions, and examples of these expansions are analysed in detail. It should be noted that for the study of these questions, some knowledge is necessary of the theory of many-valued and, in particular, algebraic functions. This is to be found in the first chapter.   Chapter V treats Hurwitz’s problem for polynomials. Although it is not connected with the preceding material, the authors are agreed that its importance for a large number of applications makes its consideration essential in a book dealing with the special problems of the theory of functions of a complex variable.   In each chapter the reader will find a large number of worked examples. These are intended to serve not only as illustrations of the theoretical conclusions, but also as models for solving independently any similar problems encountered. The engineer does not usually meet the questions dealt with in this book until his problems have been already formulated mathematically. The authors have not therefore found it necessary to consider problems with marked physical content. Nevertheless, in a number of places they have emphasized the links that exist between the mathematical theories treated and the corresponding technical disciplines.   Chapters I and II were written by B. A. Fuchs, Chapters III and IV by V.I. Levin, and Chapter V by both authors together. However, the close contact constantly maintained between them during their work on the book makes them equally responsible for the volume as a whole. 

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

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

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

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

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

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

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

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 2015.153591 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

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

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

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

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

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

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

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

Bibliographical footnotes

Theorem 1 (Stronger version) The smallest convex set which contains all the zeros of P (z) also contains the zeros of P'(z).

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

This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS. In this appendix we survey the results obtained on the topics of the book after 1970.

This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS. In this appendix we survey the results obtained on the topics of the book after 1970.

This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS. In this appendix we survey the results obtained on the topics of the book after 1970.

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 2015.161973 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 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

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

"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

"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

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)

"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

"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

"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

"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

448 p. ; 23 cm

scan of book Functions of a complex variable 1980 reprint by David Orme Tall [1970] {517'.8--loc} The four page numbers at the start of Part 2 have been omitted in the original copy.

scan of book Functions of a complex variable 1980 reprint by David Orme Tall [1970] {517'.8--loc} The four page numbers at the start of Part 2 have been omitted in the original copy.

viii, 218 p. illus. ; 23 cm

viii, 218 p. illus. ; 23 cm

viii, 218 p. illus. ; 23 cm

230 p. 24 cm