000			05024cam a22002534a 4500
999			_c1113 _d1113
001			143
005			20200820104506.0
008			021108s2004 iaua b 001 0 eng
020			_a0072872527 (alk. paper)
020			_a9780072872521
040			_cDLC
082	0	0	_a515.9 _221 _bB87717
100	1		_aBrown, James Ward.
245	1	0	_aComplex variables and applications / _cJames Ward Brown, Ruel V. Churchill.
250			_a7th ed.
260			_aBoston : _bMcGraw-Hill Higher Education, _c2004.
300			_axvi, 458 p. _bill. ; _c25 cm.
490	1		_aBrown-Churchill series
500			_aIncludes bibliographical references (p. 437-439) and index.
650		0	_aFunctions of complex variables.
700	1		_aChurchill, Ruel V.
942			_cBK
505	0		_a1. 1 complex numbers 2. Sums and products 3. Basic algebraic properties 4. Further properties 5. Moduli 6. Complex conjugates 7. Exponential form 8. Products and quotients in exponential form 9. Roots of complex numbers 10. Examples 11. Regions in the complex plane 12. 2 analytic functions 13. Functions of a complex variable 14. Mappings 15. Mappings by the exponential function 16. Limits 17. Theorems on limits 18. Limits involving the point at infinity 19. Continuity 20. Derivatives 21. Differentiation formulas 22. Cauchy–riemann equations 23. Sufficient conditions for differentiability 24. Polar coordinates 25. Analytic functions 26. Examples 27. Harmonic functions 28. Uniquely determined analytic functions 29. Reflection principle 30. 3 elementary functions 31. The exponential function 32. The logarithmic function 33. Branches and derivatives of logarithms 34. Some identities involving logarithms 35. Complex exponents 36. Trigonometric functions 37. Hyperbolic functions 38. Inverse trigonometric and hyperbolic functions 39. 4 integrals 40. Derivatives of functions w(t) 41. Definite integrals of functions w(t) 42. Contours 43. Contour integrals 44. Examples 45. Upper bounds for moduli of contour integrals 46. Antiderivatives 47. Examples 48. Cauchy–goursat theorem 49. Proof of the theorem 50. Simply and multiply connected domains 51. Cauchy integral formula 52. Derivatives of analytic functions 53. Liouville’s theorem and the fundamental theorem of algebra 54. Maximum modulus principle 55. 5 series 56. Convergence of sequences 57. Convergence of series 58. Taylor series 59. Examples 60. Laurent series 61. Examples 62. Absolute and uniform convergence of power series 63. Continuity of sums of power series 64. Integration and differentiation of power series 65. Uniqueness of series representations 66. Multiplication and division of power series 67. 6 residues and poles 68. Residues 69. Cauchy’s residue theorem 70. Using a single residue 71. The three types of isolated singular points 72. Residues at poles 73. Examples 74. Zeros of analytic functions 75. Zeros and poles 76. Behavior of f near isolated singular points 77. 7 applications of residues 78. Evaluation of improper integrals 79. Example 80. Improper integrals from fourier analysis 81. Jordan’s lemma 82. Indented paths 83. An indentation around a branch point 84. Integration along a branch cut 85. Definite integrals involving sines and cosines 86. Argument principle 87. Rouche;’s theorem 88. Inverse laplace transforms 89. Examples 90. 8 mapping by elementary functions 91. Linear transformations 92. The transformation w = 1/z 93. Mappings by 1/z 94. Linear fractional transformations 95. An implicit form 96. Mappings of the upper half plane 97. The transformation w = sin z 98. Mappings by z2 and branches of z1/2 99. Square roots of polynomials 100. Riemann surfaces 101. Surfaces for related functions 102. 9 conformal mapping 103. Preservation of angles 104. Scale factors 105. Local inverses 106. Harmonic conjugates 107. Transformations of harmonic functions 108. Transformations of boundary conditions 109. 10 applications of conformal mapping 110. Steady temperatures 111. Steady temperatures in a half plane 112. A related problem 113. Temperatures in a quadrant 114. Electrostatic potential 115. Potential in a cylindrical space 116. Two-dimensional fluid flow 117. The stream function 118. Flows around a corner and around a cylinder 119. 11 the schwarz–christoffel transformation 120. Mapping the real axis onto a polygon 121. Schwarz–christoffel transformation 122. Triangles and rectangles 123. Degenerate polygons 124. Fluid flow in a channel through a slit 125. Flow in a channel with an offset 126. Electrostatic potential about an edge of a conducting plate 127. 12 integral formulas of the poisson type 128. Poisson integral formula 129. Dirichlet problem for a disk 130. Related boundary value problems 131. Schwarz integral formula 132. Dirichlet problem for a half plane 133. Neumann problems 134. Appendixes 135. Bibliography 136. Table of transformations of regions 137. Index