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Geometric Representation of Analytic Functions

Published online by Cambridge University Press:  03 November 2016

Extract

The study of the function of a real variable is aided by the " graph " of the function. Whenever difficult analytical notions are considered, such as continuity, turning points, etc., a study of the graph enables the student to get a general view of the problem.

No such help appears to be available in teaching the theory of functions of the complex variable. A " graph " of f(x + iy) = u + iv would require a fourdimensional space. Nevertheless some representation of an analytic function seems necessary if the student is not to be discouraged by the abstract nature of the idea.

Type
Research Article
Copyright
Copyright © Mathematical Association 1945

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