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Introduction to complex analysis
Introduction to complex analysis

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2 The Cauchy–Riemann equations

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

  • find the partial derivatives of a function from double-struck cap r squared to double-struck cap r
  • use the Cauchy–Riemann equations to show that a function is not differentiable at a given point
  • use the Cauchy–Riemann equations to show that a function, such as the exponential function, is differentiable at a given point, and to find the derivative.

This section is challenging, so you may find that you do not appreciate some of the details on a first reading. Most importantly, you should try to understand the definitions, strategies and theorems, and apply them in the examples and exercises.