Analytic function theory

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Analytic function theory / by Einar Hille

版:: 2nd ed
資料種別:: 図書
出版情報:: New York : Chelsea Pub. Co., 1973
形態:: 2 v. ; 24 cm
著者名:: Hille, Einar, 1894-1980 <DA01320506>
ISBN:: 9780828402699 [0828402698] (v. 1)
9780828402705 [0828402701] (v. 2)
書誌ID:: BA42156316

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Analytic function theory. 2nd ed (v. 1 ; v. 2)
by Einar Hille , Chelsea Pub. Co. , 1977-1982

書誌詳細

注記:

Reprint of the ed. published by Ginn, Boston
Bibliography: v. 1, p. 297-298; v. 2, p. 481-483

主題:

解析関数

言語:

英語

目次情報:

Number systems / 1：

The real number system / 1.1：

Further properties of real numbers / 1.2：

The complex number system 2. The complex plane / 1.3：

Geometry of complex numbers / 2.1：

Curves and regions in the complex plane / 2.2：

Regions and convexity / 2.3：

Paths / 2.4：

The extended plane; stereographic projection 3. Fractions, powers, and roots / 2.5：

Fractional linear transformations / 3.1：

Properties of Mobius transformations / 3.2：

Powers / 3.3：

Roots / 3.4：

The function $(z^2 +1)/(2z)$ 4. Holomorphic functions / 3.5：

Complex-valued functions and continuity / 4.1：

Differentiability; holomorphic functions / 4.2：

The Cauchy-Riemann equations / 4.3：

Laplace's equation / 4.4：

The inverse function / 4.5：

Conformal mapping / 4.6：

Function spaces 5. Power series / 4.7：

Infinite series / 5.1：

Operations on series / 5.2：

Double series / 5.3：

Convergence of power series / 5.4：

Power series as holomorphic functions / 5.5：

Taylor's series / 5.6：

Singularities; noncontinuable power series 6. Some elementary functions / 5.7：

The exponential function / 6.1：

The logarithm / 6.2：

Arbitrary powers; the binomial series / 6.3：

The trigonometric functions / 6.4：

Inverse trigonometric functions 7. Complex integration / 6.5：

Integration in the complex plane / 7.1：

Cauchy's theorem / 7.2：

Extensions / 7.3：

Cauchy's integral / 7.4：

Cauchy's formulas for the derivatives / 7.5：

Integrals of the Cauchy type / 7.6：

Analytic continuation: Schwarz's reflection principle / 7.7：

The theorem of Morera / 7.8：

The maximum principle / 7.9：

Uniformly convergent sequences of holomorphic functions 8. Representation theorems / 7.10：

The maximum modulus / 8.1：

The Laurent expansion / 8.3：

Isolated singularities / 8.4：

Meromorphic functions / 8.5：

Infinite products / 8.6：

Entire functions / 8.7：

The Gamma function 9. The calculus of residues / 8.8：

The residue theorem / 9.1：

The principle of the argument / 9.2：

Summation and expansion theorems / 9.3：

Inverse functions / 9.4：

Some properties of point sets / Appendix A：

Some properties of polygons / Appendix B：

On the theory of integration / Appendix C：

Bibliography

Index

Number systems / 1：

The real number system / 1.1：

Further properties of real numbers / 1.2：

The complex number system 2. The complex plane / 1.3：

Geometry of complex numbers / 2.1：

Curves and regions in the complex plane / 2.2：

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