# Complex variables and applications / James Ward Brown, Ruel V. Churchill.

Material type: TextSeries: Publication details: Boston : McGraw-Hill Higher Education, 2004.Edition: 7th edDescription: xvi, 458 p. ill. ; 25 cmISBN:- 0072872527 (alk. paper)
- 9780072872521

- 515.9 21 B87717

Item type | Current library | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|

Books | UE-Central Library | 515.9 B87717 (Browse shelf(Opens below)) | Available | T143 |

Includes bibliographical references (p. 437-439) and index.

1. 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

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