Theory of Complex Functions

Historical Introduction. - Chronological Table. - A. Elements of Function Theory. - 0. Complex Numbers and Continuous Functions. - 1. Complex-Differential Calculus. - 2. Holomorphy and Conformality. Biholomorphic Mappings. - 3. Modes of Convergence in Function Theory. - 4. Power Series. - 5. Elementary Transcendental Functions. - B. The Cauchy Theory. - 6. Complex Integral Calculus. - 7. The Integral Theorem Integral Formula and Power Series Development. - C. Cauchy-Weierstrass-Riemann Function Theory. - 8. Fundamental Theorems about Holomorphic Functions. - 9. Miscellany. - 10. Isolated Singularities. Meromorphic Functions. - 11. Convergent Series of Meromorphic Functions. - 12. Laurent Series and Fourier Series. - 13. The Residue Calculus. - 14. Definite Integrals and the Residue Calculus. - Short Biographies o/Abel Cauchy Eisenstein Euler Riemann and Weierstrass. - Photograph of Riemann's gravestone. - Literature. - Classical Literature on Function Theory Textbooks on Function Theory Literature on the History of Function Theory and of Mathematics Symbol Index. - Name Index. - Portraits of famous mathematicians 3. Language: English