# Analytic Function Theory, Volume I

###### Einar Hille
Publisher:
American Mathematical Society/Chelsea
Publication Date:
1959
Number of Pages:
308
Format:
Hardcover
Edition:
2
Price:
32.00
ISBN:
0-8284-0269-8
Category:
Monograph
BLL Rating:

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

There is no review yet. Please check back later.

• 1. Number systems: 1.1 The real number system; 1.2 Further properties of real numbers; 1.3 The complex number system
• 2. The complex plane: 2.1 Geometry of complex numbers; 2.2 Curves and regions in the complex plane; 2.3 Regions and convexity; 2.4 Paths; 2.5 The extended plane; stereographic projection
• 3. Fractions, powers, and roots: 3.1 Fractional linear transformations; 3.2 Properties of Möbius transformations; 3.3 Powers; 3.4 Roots; 3.5 The function $(z^2 +1)/(2z)$
• 4. Holomorphic functions: 4.1 Complex-valued functions and continuity; 4.2 Differentiability; holomorphic functions; 4.3 The Cauchy-Riemann equations; 4.4 Laplace's equation; 4.5 The inverse function; 4.6 Conformal mapping; 4.7 Function spaces
• 5. Power series: 5.1 Infinite series; 5.2 Operations on series; 5.3 Double series; 5.4 Convergence of power series; 5.5 Power series as holomorphic functions; 5.6 Taylor's series; 5.7 Singularities; noncontinuable power series
• 6. Some elementary functions: 6.1 The exponential function; 6.2 The logarithm; 6.3 Arbitrary powers; the binomial series; 6.4 The trigonometric functions; 6.5 Inverse trigonometric functions
• 7. Complex integration: 7.1 Integration in the complex plane; 7.2 Cauchy's theorem; 7.3 Extensions; 7.4 Cauchy's integral; 7.5 Cauchy's formulas for the derivatives; 7.6 Integrals of the Cauchy type; 7.7 Analytic continuation: Schwarz's reflection principle; 7.8 The theorem of Morera; 7.9 The maximum principle; 7.10 Uniformly convergent sequences of holomorphic functions
• 8. Representation theorems: 8.1 Taylor's series; 8.2 The maximum modulus; 8.3 The Laurent expansion; 8.4 Isolated singularities; 8.5 Meromorphic functions; 8.6 Infinite products; 8.7 Entire functions; 8.8 The Gamma function
• 9. The calculus of residues: 9.1 The residue theorem; 9.2 The principle of the argument; 9.3 Summation and expansion theorems; 9.4 Inverse functions
• Appendix A: Some properties of point sets
• Appendix B: Some properties of polygons
• Appendix C: On the theory of integration
• Bibliography
• Index