CHAPTER II - THE USE OF COMPLEX FUNCTIONS 

 IN HYDRODYNAMICS 



19. Complex Numbers 33 



20. Some Common Functions of z 36 



21. Powers of z 37 



22. Regular Functions of a Complex Variable 38 



23. Conformal Representation or Mapping 39 



24. Examples of Conformal Transformations 42 



25. Relation of Regular Functions to Two-Dimensional 



Irrotational Flow 46 



26. The Transformation of Irrotational Motions 50 



27. The Laurent Series 51 



28. Complex Integration 52 



29. The Cauchy Integral Theorem 53 



30. Singular Points and Residues 56 



31. The Schwarz-Christoffel Transformation 57 



32. The Hyperbolic Functions 66 



33. Some Series 69 



CHAPTER III - CASES OF TWO-DIMENSIONAL FLOW 



34. Notation and Form of Presentation 70 



SOME SIMPLE TYPES OF FLOW 74 



35. Uniform Motion 74 



36. Hyperbolic Flow 75 



37. Line Dipole 75 



38. Line Quadrupole 78 



39. Flow in an Angle 79 



40. Logarithmic Flow 82 



V 



