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.
Inhaltsverzeichnis
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.
