"Complex Variables Class Notes" Webpage

Complex Variables Class Notes
Complex Variables and Applications, 9th Edition, J. W. Brown and R. V. Churchill. Brown and Churchill, Complex Variables Book

Brown and Churchill, Complex Variables Book

Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors).

Chapter 7. Applications of Residues.
Chapter 8. Mapping by Elementary Functions.
Chapter 9. Conformal Mappings.
Chapter 10. Applications of Conformal Mappings.
Chapter 11. The Schwarz-Christoffel Transformation.
Chapter 12. Integral Formulas of the Poisson Type.

Chapter 7. Applications of Residues.

Section 85. Evaluation of Improper Integrals.
Section 86. Example.
Section 87. Improper Integrals from Fourier Analysis.
Section 88. Jordan's Lemma.
Section 89. An Indented Path.
Section 90. An Indentation Around a Branch Point.
Section 91. Integrating Along a Branch Cut.
Section 92. Definite Integrals Involving Sines and Cosines.
Section 93. Argument Principle.
Section 94. Rouche's Theorem.
Section 95. Inverse Laplace Transforms.
Study Guide 7.

Chapter 8. Mapping by Elementary Functions.

Section 96. Linear Transformatons.
Section 97. The Transformation w = 1/z.
Section 98. Mappings by 1/z.
Section 99. Linear Fractional Trnasformations.
Section 100. An Implicit Form.
Section 101. Mappings of the Upper Half Plane.
Section 102. Examples.
Section 103. Mappings by the Exponential Function.
Section 104. Mapping Vertical Line Segments by w = sin z.
Section 105. Mapping Horizontal Line Segments by w = sin z.
Section 106. Some Related Mappings.
Section 107. Mappings by z².
Section 108. Mappings by Branches of z^1/2.
Section 109. Square Roots of Polynomials.
Section 110. Riemann Surfaces.
Section 111. Surfaces for Related Functions.
Study Guide 8.

Chapter 9. Conformal Mappings.

Section 112. Preservation of Angles and Scale Factors. Section 9.112 notes
Section 113. Further Examples. Section 9.113 notes
Section 114. Local Inverses. Section 9.114 notes
Section 115. Harmonic Conjugates. Section 9.115 notes

Supplement. Proofs of Theorems in Section 9.115. Beamer file of Section 9.115 proofs and examples
Supplement. Printout of the Proofs of Theorems in Section 9.115. Print file of Section 9.115 proofs and examples

Section 116. Transformations of Harmonic Functions. Section 9.116 notes

Supplement. Proofs of Theorems in Section 9.116. Beamer file of Section 9.116 proofs and examples
Supplement. Printout of the Proofs of Theorems in Section 9.116. Print file of Section 9.116 proofs and examples

Section 117. Transformations of Boundary Conditions. Section 9.117 notes

Supplement. Proofs of Theorems in Section 9.117. Beamer file of Section 9.117 proofs and examples
Supplement. Printout of the Proofs of Theorems in Section 9.117. Print file of Section 9.117 proofs and examples

Study Guide 9.

Chapter 10. Applications of Conformal Mappings.

Section 118. Steady Temperatures. Section 10.118 notes
Section 119. Steady Temperatures in a Half Plane. Section 10.119 notes
Section 120. A Related Problem. Section 10.120 notes (This section includes the Beer in the Snow boundary value problem.)
Section 121. Temperatures in a Quadrant. Steady Temperatures in a Half Plane. Section 10.121 notes
Section 122. Electrostatic Potential.
Section 123. Examples.
Section 124. Two-Dimensional Fluid Flow.
Section 125. The Stream Function.
Section 126. Flows Around a Corner and Around a Cylinder.
Study Guide 10.

Chapter 11. The Schwarz-Christoffel Transformation.

Section 127. Mapping the Real Axis Onto a Polygon.
Section 128. Schwarz-Christoffel Transformation.
Section 129. Triangles and Rectangles.
Section 130. Degenerate Polygons.
Section 131. Fluid Flow in a Channel Through a Slit.
Section 132. Flow in a Channel With an Offset.
Section 133. Electrostatic Potential About an Edge of a Conducting Plate.
Study Guide 11.

Chapter 12. Integral Formulas of the Poisson Type.

Section 134. Poisson Integral Formula.
Section 135. Dirichlet Problem for a Disk.
Section 136. Examples.
Section 137. Related Boundary Value Problems.
Section 138. Schwarz Integral Formula.
Section 139. Dirichlet Problem for a Half Plane.
Section 140. Neumann Problems.
Study Guide 12.

Return to Bob Gardner's home page