This course on complex functions is distinguished by consistently using phaseportraits, a special color representation which visualizes functions as images. The text introduces the basic concepts of complex analysis, and, parallel to a systematic investigation of analytic and meromorphic functions, readers learn how properties of a function are reflected in and can be recovered from its phase portrait. The approach emphasizes constructive aspects, it is intuitive, and requires only basic knowledge of calculus. More advanced readers will get a fresh view on classical results and may be inspired by the pictures to new and challenging questions. First introduction to complex functions systematically using phase portraits (which are expected to become an indispensable tool for exploring complex functions in teaching, mathematical research and applications alike). Reorganization of the traditional material covered by textbooks in complex analysis andemphasis on special aspects of the topic. A companion to rather than a substitute for existing textbooks on complex analysis, although mostly self-contained. Enhances intuitive understanding of basic concepts and special functions byvisualizing complex functions by phase plots. Complete text equipped with color illustrations. INDICE: Preface. 1 Introduction. 2 Complex Functions. 3 Analytic Functions. 4 Complex Calculus. 5 Conformal Mapping. 6 Special Topics and Applications. 7 Phase Diagrams. 8 An Atlas of Functions.
- ISBN: 978-3-0348-0179-9
- Editorial: Springer Basel
- Encuadernacion: Rústica
- Páginas: 200
- Fecha Publicación: 14/03/2012
- Nº Volúmenes: 1
- Idioma: Inglés