复变函数论-第二版 本书特色
马立新编著的这本《复变函数论（第2版）》共6 章，主要内容包括复数与复变函数、解析函数、 复变函数的积分、级数、留数及其应用和共形映射等 ，较全面、 系统地介绍了复变函数的基础知识。内容处理上重点 突出、叙述 简明，每节末附有适量习题供读者选用，适合高等师 范院校数学 系及普通综合性大学数学系高年级学生使用。
复变函数论-第二版 目录
前言chapter i complex numbers and functions 1 complex numbers 1.1 complex number field 1.2 complex plane 1.3 modulus, conjugation, argument, polar representation 1.4 powers and roots of complex numbers exercises 2 regions in the complex plane 2.1 some basic concept 2.2 domain and jordan curve exercises 3 functions of a complex variable 3.1 the concept of functions of a complex variable 3.2 limits and continuous exercises 4 the extended complex plane and the point at infinity 4.1 the spherical representation, the extended complex plane 4.2 some concepts in the extended complex plane exerciseschapter ii analytic functions 1 the concept of the analytic function 1.1 the derivative of the functions of a complex variable 1.2 analytic functions exercises 2 cauchy-riemann equations exercises 3 elementary functions 3.1 the exponential function 3.2 trigonometric functions 3.3 hyperbolic functions exercises 4 multi-valued functions 4.1 the logarithmic function 4.2 complex power functions 4. 3 inverse trigonometric and hyperbolic functions exerciseschapter iii complex integration 1 the concept of contour integrals 1.1 integral of a complex function over a real interval 1.2 contour integrals exercises cauchy-goursat theorem 2.1 cauchy theorem 2.2 cauchy integral formula 2.3 derivatives of analytic functions 2.4 liouville's theorem and the fundamental theorem of algebra exercises harmonic functions exerciseschapter iv series 1 basic properties of series 1.1 convergence of sequences 1.2 convergence of series 1.3 uniform convergence exercises 2 power series exercises 3 taylor series exercises 4 laurent series exercises 5 zeros of an analytic functions and uniquely determined analytic functions 5.1 zeros of analytic functions 5.2 uniquely determined analytic functions 5.3 maximum modulus principle exercises 6 the three types of isolated singular points at a finite point exercises 7 the three types of isolated singular points at a infinite point exerciseschapter v calculus of residues 1 residues 1.1 residues 1.2 cauchy's residue theorem 1.3 the calculus of residue exercises 2 applications of residue 2.1 the type of definite integral □ 2.2 the type of improper integral □ 2.3 the type of improper integral □ exercises 3 argument principle exerciseschapter vi conformal mappings 1 analytic transformation 1.1 preservation of domains of analytic transformation 1.2 conformality of analytic transformation exercises 2 rational functions 2.1 polynomials 2.2 rational functions exercises 3 fractional linear transformations exercises 4 elementary conformal mappings exercises 5 the riemann mapping theorem exercisesappendix appendix 1 appendix 2answersbibliography
