Abstract
Abstract This chapter highlights vector fields. The vector field concept remedies a significant defect in the mapping point of view. Although one can learn a lot about a mapping by looking at the images of specific shapes, one does not get a feel for its overall behaviour. However, if one lets their one’s eyes roam over the vector field of a complex function they do get such a view, in much the same way as one can survey the behaviour of a real function by scanning its graph. Just as a complex mapping determines a vector field, so a vector field determines a mapping-the two concepts are equivalent. The chapter then looks at the connection between winding numbers and vector fields, before considering the Poincaré-Hopf Theorem.
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