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Introduction to complex analysis
Introduction to complex analysis

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1 Derivatives of complex functions

After working through this section, you should be able to:

  • use the definition of derivative to show that a given function is differentiable, and to find its derivative
  • use the Combination Rules for differentiation to differentiate polynomial and rational functions
  • use various strategies to show that a given function is not differentiable at a point
  • interpret the derivative of a complex function at a point as a rotation and a scaling of a small disc centred at the point.