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

14

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

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

xxiv, 855, [1] p. 27 cm

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

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 2015.153725 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

230 p. 24 cm

230 p. 24 cm

xxii, 682 p. 28 cm

xxii, 682 p. 28 cm

"On the Theory of Functions of a Complex Variable" is an article from The Annals of Mathematics, Volume 8 . 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-1967935

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

xiii, 288 p. 25 cm

xiii, 288 p. 25 cm

viii, 218 p. illus. ; 23 cm

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

"Forsyth's Theory of Functions of a Complex Variable" is an article from The Annals of Mathematics, Volume 7 . 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-1967892

"Forsyth's Theory of Functions of a Complex Variable" is an article from The Annals of Mathematics, Volume 7 . 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-1967892

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.

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

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

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

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

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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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.

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

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

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

Classical reference on Theory of functions of complex variable

Classical reference on Theory of functions of complex variable

Classical reference on Theory of functions of complex variable

Bibliographical footnotes

Bibliographical footnotes

Bibliographical footnotes

Bibliographical footnotes

Title: Lectures on the Theory of Functions of a Complex Variable: Volume II: Geometric Theory Author(s): G. Sansone; J. Gerretsen Series: Lectures on the Theory of Functions of a Complex Variable 2 Language: English Year: 1968 Publisher: Springer ISBN: 9028609040, 9789028609044 Pages: 700 (bibliographic) / 709 (file) Format: PDF File size: 21.32 Mb (22354934 bytes) Time added / time modified: 2023-03-24 18:03:05 Commentary: OCR'd with ABBYY Finereader (not proofread). The covers is blank so I generated one.

1Problems of Philosophy

By Bertrand Russell

The Problems of Philosophy is one of Bertrand Russell's attempts to create a brief and accessible guide to the problems of philosophy. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics.<br></br>Russell guides the reader through his famous distinction between "knowledge by acquaintance and knowledge by description" and introduces important theories of Plato, Aristotle, René Descartes, David Hume, John Locke, Immanuel Kant, Georg Hegel and others to lay the foundation for philosophical inquiry by general readers and scholars alike. (Summary from Wikipedia)

LibriVox volunteers bring you 14 different recordings of <em>The Hour of Twilight</em> by George William Russell, published in "Collected Poems" in 1913. This was the weekly poetry project for the week of November 18th, 2007.

3Forgiveness (Russell)

By George William Russell

LibriVox volunteers bring you 19 recordings of <em>Forgiveness</em> by George William Russell. This was the weekly poetry project for June 7th, 2009.

4Frozen Pirate

By William Clark Russell

Sailing adventure with storms, icebergs, shipwrecks, treasure, and the reawakening of a pirate frozen in suspended animation for nearly fifty years (Summary by P. Cunningham)

5Proposed Roads to Freedom

By Bertrand Russell

Bertrand Russell, 3rd Earl Russell (1872 – 1970) was a British philosopher, logician, mathematician, political activist and Nobel laureate. He led the British "revolt against idealism" in the early 1900s and is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his protégé Ludwig Wittgenstein. In this book, written in 1918, he offers his assessment of three competing streams in the thought of the political left: Marxian socialism, anarchism and syndicalism.<br /> (Summary by Wikipedia/Carl Manchester)

We meet Miss Lucretia Lane as she is dressing for her marriage to Captain Francis Reynolds of the British Merchant Service. Though he loves her truly, she has severe misgivings. She goes through with the wedding in spite of this, but refuses to live with her new husband, and cannot be enticed or cajoled to do so. Then on the day the Captain is scheduled to ship out, she receives word that he has been gravely injured and his dying request is to see his wife. She flies to his side... and thus begins an adventure spanning eight years - love, loathing, shipwreck, love lost, and redemption. (Summary by P. Cunningham and Nadine Eckert-Boulet)

This is a collection of short stories of mystery and romance, set at sea, in the times of the great sea voyages.

8Analysis of Mind

By Bertrand Russell

A neat work on philosophy of mind by the 20th century analytic philosopher Bertrand Russell. (Summary by sidhu177)

9Marriage at Sea

By William Clark Russell

Herbert Barclay is desperately in love with Grace Bellassys, but a number of factors stand in the way of their happiness, the biggest of which is the person of Lady Amelia Roscoe, Grace's guardian. Lady Amelia has several objections to the union, one of which is the fact that Herbert is not a Papist, and to separate the two young people, she has sent Grace to school in France. The two decide to elope, but this is just the start of the adventure... - Summary by Carolin

10Last Entry

By William Clark Russell

This is a sea-faring novel set in 1837. A wealthy former seaman from London and his daughter, who is engaged to be married, set sail on his newly restored schooner, headed for the equator for the purpose of restoring his health. Also aboard are a captain and crew. Soon, distractions, diversions, discontent and much more occur. William Clark Russell (1844–1911) was an English writer best known for his nautical novels. ~ Lee Smalley

'The Philosophy of Logical Atomism' is a series of lectures by Bertrand Russell (1872-1970) that touches on numerous topics, including the nature of propositions, the relations of propositions to facts and of different types of words to the varieties of things, what kinds of facts there are, existence, monism and pluralism, and aspects of philosophical logic and of reference. Guiding the lectures, at least according to Russell's headnote to his lectures, is Russell's intent to fully flesh out ideas he learned from his former pupil, Ludwig Wittgenstein (1889-1951). - Summary by Landon D. C. Elkind

Bertrand Russell gave the Lowell Lectures in March and April of 1914; these lectures produced 'Our Knowledge of the External World'. Russell attempts to analyze the relationship of the crude data of our senses to the notions of physics such as space, time, and matter. Russell takes his analysis to illustrate the method of logical analysis used to such wonderful effect by thinkers in the late nineteenth-century to the notions of continuity, infinity, and the infinitesimal. These analyses effected a new epoch of clarity in the philosophy of mathematics; Russell hopes that a similar new age of clarity can be effected in the rest of philosophy through logical analysis; here, he undertakes the first stages of this analysis in the philosophy of physics. Summary by Landon D. C. Elkind.

Bertrand Russell wrote 'Introduction to Mathematical Philosophy' while imprisoned for protesting Britain's involvement in World War I. Russell summarizes the significance of the momentous work of mathematicians in the late nineteenth-century. He further describes his own philosophy of mathematics, Logicism (the view that all mathematical truths are logical truths), and his earlier, influential work solving the paradoxes that plagued mathematical foundations, which crystallized after ten years of dogged effort into the co-authored (with Alfred North Whitehead), three-volume 'Principia Mathematica'. Russell emphasizes the importance of a doctrine of types, the truth of Logicism, and the clarity brought to the philosophy of mathematics by the method of logical analysis. (summary by Landon D. C. Elkind)

This anthology collects a number of fascinating strands of Bertrand Russell's thought. "Mathematics and the Metaphysicians" details the impact of the 1900 World Congress of Philosophers on Russell's development and the hope that new methods in mathematics could be applied to the solution of ancient philosophical problems. Many of the subsequent essays show the evolution of this hope as Russell worked on the foundations of mathematics and applied the new methods to the reconstruction of physical objects on the basis of sense-data, and the redefinition of matter and cause. (Landon D. C. Elkind)

15Problem of China

By Bertrand Russell

In 1920-21 Bertrand Russell lived and taught in Peking (Beijing), publishing this book on his return to England. In 1920 he had visited Bolshevik Russia, talked to Lenin, and was unimpressed by what he had seen. China, however, was another matter. Like many travelers, he often saw what he wanted to see, and after Europe’s Great War, he found many signs of hope in China. In that country, he was welcomed by the young intellectuals who saw him as a representative of modern and scientific thought. They, however, were trying to cast off much of the old tradition that they thought held China back, and they were often opposed to Russell’s urging that they hold on to much of their own tradition, which he saw as superior to that of Europe, particularly after the terrible slaughter of 1914-18 on the continent. His work is very much a product of its time, and today, almost a century later, many are still trying to explain China -- a very different China from Russell's -- to an outside world. (Nicholas Clifford)

16Political Ideals

By Bertrand Russell

This is a book by the famous 20th century British philosopher Bertrand Russell on Political Ideals. It was written during the course of World War 1 and contains a critique on the politico economic situation of then Europe. What is interesting is that some of his beliefs are still relevant today. (Summary by Sid)

William Clark Russell is well-known for his maritime stories, for which he could draw upon his own experiences as a sailor in the British Navy. This is one of the finest examples of his maritime ghost stories.<br></br>Everyone knows the story of the ghostly ship, the Flying Dutchman, which is cursed and doomed to sail the seven seas forever, bringing destruction to anyone crossing its path. Geoffrey Fenton, narrator of this story, is one of those unlucky persons who do cross this ship's path, and who even gets captured by it. When he finds himself on the famous Death Ship, the adventure of his life begins, including deadly storms, pirates, and a very particular beautiful damsel in distress. - Summary by Carolin

In this piece, Bertrand Russell offers an account of propositions. This essay has been widely regarded as a turning point in Russell's thought: fresh from his prison sentence, during which he read numerous works of psychology, he now rejects the existence of the unitary, lasting metaphysical subject and the act-object analysis of sensation. He here embraces the view advocated by American philosophers like William James, namely, neutral monism. This far-ranging essay includes a lengthy discussion of behaviorism and of the structure of facts, complete with an endorsement of negative facts and criticisms of attempts to avoid them. - Summary by Landon D. C. Elkind

This 1912 book remains among the most widely-used and well-written introductions to philosophy in English. It was aimed to be an accessible introduction to philosophy for the average shopkeeper in England in 1912. Despite its accessibility It has engaged scholarly philosophical commentators on a range of issues raised in the work. Above all it conveys in easy and witty manner the philosophical frame of mind to those that have never encountered it before. It was almost immediately, and remains today, a classic. <i>This recording is dedicated to Jill Evans, Esq.</i> (Landon D. C. Elkind)

George William Russell -- better known by his pen name "A.E." -- was an Irish writer, poet and mystic, a lifelong friend of William Butler Yeats, and an original member of Ireland's Theosophical Society. In a letter to a friend, penned several years before he died, he wrote: "I know no mechanism is going to solve the world's problems. Nothing will, except the spiritual life." This volume of poems contains his first published work and reflects on the mysteries of nature and the divine, of life and the universe. (Summary by Nemo)

This is a book of remarkable nautical ghost and horror stories written by William Clark Russell in 1893. The stories are for the most part set on ships and bring the reader on board for ghostly nights, wonderful sights, and strange occurrences. (Summary by Carolin)

22One Hundred Years In Yosemite: The Story Of A Great Park And Its Friends

By Carl Parcher Russell

This recording of the 1931 (1947 second edition) book about Yosemite National Park comprises the narrative text about the Park from its discovery by non-natives in the Indian War of 1851 to the mid-twentieth century. The printed book contains dozens of early photographs and drawings, as well as an extensive timeline and bibliography, which are not here recorded. The author (1894-1967) was an ecologist, historian, and administrator. He was an officer of the U.S. National Park Service for thirty four years, serving as the Chief Naturalist of Yosemite from 1923-1929 and later as Park Superintendent. - Summary by David Wales

This book records Bertrand Russell's impressions of the new regime after a 1920 visit to Russia following the 1917 Bolshevik Revolution, including his meetings with Lenin, Trostky, and Gorky. It includes a chapter that was authored by Dora Black, educational theorist and feminist author, and Russell's spouse. This chapter was unfortunately removed in the second edition, which was issued after Dora and Bertrand divorced. This recording is dedicated to my darling wife, Jill. Happy Hanukkah and Happy 2020! - Summary by Landon D. C. Elkind

24Frozen Pirate (version 2)

By William Clark Russell

Drawing on his own experience as a merchant seaman, Russell gives us the fictionalized narrative of one Paul Rodney who found an icebound vessel in the South Atlantic, while captaining a pirate ship. Russell has been hailed as the pre-eminent English writer of his ilk, compared to such American writers as Melville and Dana. - Summary by Lynne Thompson

25My Danish Sweetheart Volume 1

By William Clark Russell

Young Hugh Tregarthen has grown up in a seafaring Cornish family, but is not born to follow the family tradition. Against his mother's wishes, he is coxswain of a lifeboat -- an important job along the treacherous coastline, which makes his mother proud, despite her misgivings. One morning, as he sets out for his boat Janet, invalid Mrs. Tregarthen warns her son of an ominous dream she had the previous night. He laughs it off... but sometimes, dreams come true. - Summary by Lynne Thompson

Six out of seven essays appearing here were reprinted from other publications; indeed, this 1910 collection went out of print, so that two of the essays occurring here were reprinted in Russell's 1917 "Mysticism and Logic, and Other Essays". Nonetheless, this essay records Russell's thinking at a critical juncture, just before the publication of Volume I of the co-authored "Principia Mathematica" and just after the passing of the American pragmatist, William James. These essays record Russell's reactions to pragmatism and its theory of truth, as well as the ethical aspects of philosophy suitable for co-existing alongside the new logical method in philosophy, announced subsequently in the 1914 "Our Knowledge of the External World: as a Field for Scientific Method in Philosophy". - Summary by Landon D. C. Elkind

27My Danish Sweetheart Volume 2

By William Clark Russell

Volume 2 begins as our hero winds up his story. But the question remains, what happened to the other boat? Hugh and Helga have been picked up by a small boat, which is, apparently, headed for Australia against all seafaring wisdom. Too far from the coast to backtrack, the couple set out on an unanticipated journey.

A short introductory book about atoms, subatomic particles and new (at that time) physics theories.

29Yarn of Old Harbour Town

By William Clark Russell

This novel opens in 1805, during the Napoleonic Wars between England and France. A retired sailor, Captain Acton, reminisces about his time at sea now he lives on shore and wonders about a ship seen burning at sea the previous night. But there is one more voyage for the Captain, this time taking his daughter Lucy. As all sailors know, a woman on board brings bad luck.

The ABC of Relativity clearly and engagingly explains Einstein's Theory of Relativity to the layperson. It is considered to be a significant contribution to the popularization of science. Its author, Bertrand Russell, was an acclaimed British mathematician, philosopher and logician. Please note that in a few of the chapters, diagrams are included which clarify the author's discourse. The listener may wish to consult a published text to refer to these diagrams. (Summary by Ciiufi Galeazzi)

31Wreck of the Corsaire

By William Clark Russell

This book was published in 1897. When cabin passenger Mr. Catesby climbs into the rigging of the Ruby in search of cooler air, he is struck full in the face and chest by an errant seabird bearing a sealed tin box tied about its neck. What he finds in that box leads him to unexpected encounters with a wrecked ship, chests of gold, thirst, desperation, and some curiously courteous cutlass-carrying cutthroats (sorry). It projects a rather different take on the familiar bloodstained swashbuckling sea story. - Summary by Steven Seitel

A relatively brief history of the life and conquests of Alexander the Great. - Summary by KevinS