Titlebook: Visual Complex Functions; An Introduction with Elias Wegert Textbook 2012 Springer Basel 2012 complex functions.phase portraits

軟弱

Complex Calculus,s based. Though there is . no difference between the definitions of differentiability for real and complex functions, the . of these two notions is quite different. This distinction manifests itself in the famous ., a system of two partial differential equations which couple the real and the imaginary parts of a complex differentiable function.

噴油井

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judicial

https://doi.org/10.1007/978-3-0348-0180-5complex functions; phase portraits

服從

Complex Functions,The functions we shall be exploring in this book are complex-valued functions of a single complex variable. When we speak of ., we do not necessarily mean that these functions are analytic, although emphasis will be placed on this special and extremely important class.

滔滔不絕地說

Conformal Mappings,The focus of this chapter is on geometric aspects: complex functions will be considered as mappings between subsets of two complex planes which transplant objects from one plane to the other.

Genteel

Riemann Surfaces,In Section 3.6 we have seen that the process of analytic continuation may result in “multiple-valued” functions. Notwithstanding their name, these objects are not ordinary functions and must be handled with care.

抗體

Elias WegertFirst 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

ligature

Construction Principles,where we prove ., a compactness criterion for families of analytic functions. This result is a key ingredient of many existence proofs and will be applied in Section 6.4 to derive the Riemann mapping theorem.

Cuisine

ng complex functions in teaching, mathematical research and .This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains.

吸引人的花招

Getting Acquainted,ions can be depicted easily in a plane, the graph of a complex function in one variable is a surface in four-dimensional space. Since our imagination is trained in three dimensions, most of us have difficulties in ‘seeing’ such an object.