The Schwarz Function and Its Applications

 1. Prologue 2. Conjugate Coordinates in the Plane 3. Elementary Geometrical Facts 4. The Nine-Point Circle 5. The Schwarz Function for an Analytic Arc 6. Geometrical Interpretation of the Schwarz Function; Schwarzian Reflection 7. The Schwarz Function and Differential Geometry 8. Conformal Maps, Reflections, and their Algebra 9. What Figure is the Power of a Circle? 10. Properties in the Large of the Schwarz Function 11. Derivatives and Integrals 12. Application to Elementary Fluid Mechanics 13. The Schwarz Function and the Dirichlet Problem 14. Schwarz Functions of Specified Type 15. Schwarz Functions and Iterations 16. Schwarz Functions of Specified Type 17. Schwarz Functions and Iterations 18. Dictionary of Functional Relationships 19. Bibliographical and Supplementary Notes 20. Bibliography 21. Index