XVI 
CONTENTS 
CHAPTER XX 
1. 
COMPLEX QUANTITIES AND THE THEORY OF FUNCTIONS 
The Age of Fable .......... 
PAGE 
491 
2. 
Geometrical Representations ....... 
493 
3. 
Inequalities 
497 
4. 
Powers and Roots . . . . 
497 
5. 
The Function e* ........ 
499 
6. 
The Function log z ........ 
501 
7. 
The Functions sin z, cos z, tan z, etc. ..... 
503 
8. 
The Inverse Trigonometric Function, sin -1 z, tan -1 z, etc. 
505 
9. 
The Hyperbolic Functions 
506 
10. 
Limits and Continuity . . . . 
510 
11. 
The Derivative ......... 
511 
12. 
The Cauchy-Riemann Differential Equations 
512 
13. 
Laplace’s Equation, Au = 0 . 
515 
14. 
Cauchy’s Integral Theorem ....... 
516 
15. 
Cauchy’s Integral Formula ....... 
518 
16. 
Taylor’s Theorem ......... 
520 
17. 
Multiple-Valued Functions ....... 
523 
18. 
Conformal Mapping ........ 
523 
19. 
Flow of Heat or Electricity. Irrotational Fluid Motion 
525 
Index 
527