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| E.B．Saff 1964年子佐治亚理工学院获得学士学位，1968年子马里兰大学获得博士学位，现为范德比尔特大学数学系教授，构造逼近中心教授、主任。他主要从事逼近论、位势论、复分析和数值分析等领域的研究。 A.D．Snider 1962年于麻省理工学院获得数学学士学位，1966年子波士顿大学获得物理学硕士学位，1971年子纽约大学数学系获得博士学位，现为南佛罗里达大学电子工程系教授。他主要从事光谱分析、最优化、电子学与电磁学的数学建模及通信理论等方面的研究。 .. << 查看详细 |
| preface 1 complex numbers 1.1 the algebra of complex numbers 1.2 point representation of complex numbers 1.3 vectors and polar forms 1.4 the complex exponential 1.5 powers and roots 1.6 planar sets 1.7 the riemann sphere and stereographic projection summary 2 analytic functions 2.1 functions of a complex variable 2.2 limits and continuity 2.3 analyficity 2.4 the cauchy-riemann equations 2.5 harmonic functions 2.6 *steady-state temperature as a harmonic function 2.7 *iterated maps: julia and mandelbrot sets summary 3 elementary functions .3.1 polynomials and rational functions 3.2 the exponential, trigonometric, and hyperbolic functions 3.3 the logarithmic function 3.4 washers, wedges, and walls 3.5 complex powers and inverse trigonometric functions 3.6 *application to oscillating systems summary 4 complex integration 4.1 contours 4.2 contour integrals 4.3 independence of path 4.4 cauchy's integral theorem 4.4a deformation of contours approach 4.4b vector analysis approach 4.5 cauchy's integral formula and its consequences 4.6 bounds for analytic functions 4.7 *applications to harmonic functions summary 5 series representations for analytic functions 5.1 sequences and series 5.2 taylor series 5.3 power series 5.4 *mathematical theory of convergence 5.5 laurent series 5.6 zeros and singularities 5.7 the point at infinity 5.8 *analytic continuation summary 6 residue theory 6.1 the residue theorem 6.2 trigonometric integrals over [0, 2] 6.3 improper integrals of certain functions over (-∞,∞) 6.4 improper integrals involving trigonometric functions 6.5 indented contours 6.6 integrals involving multiple-valued functions 6.7 the argument principle and roucht's theorem summary 7 conformal mapping 7.1 invariance of laplace's equation 7.2 geometric considerations 7.3 mtbius transformations 7.4 mtbius transformations, continued 7.5 the schwarz-christoffel transformation 7.6 applications in electrostatics, heat flow, and fluid mechanics 7.7 further physical applications of conformal mapping summary 8 the transforms of applied mathematics 8.1 fourier series (the finite fourier transform) 8.2 the fourier transform 8.3 the laplace transform 8.4 the z-transform 8.5 cauchy integrals and the hilbert transform summary a numerical construction of conformal maps a.1 the schwarz-christoffel parameter problem a.2 examples a.3 numerical integration a.4 conformal mapping of smooth domains a.5 conformal mapping software b table of conformal mappings b.1 mobius transformations b.2 other transformations answers to odd-numbered problems index |
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