# Course conclusion

Well done on completing this course, Introduction to complex analysis. As well as being able to understand the terms and definitions, and use the results introduced, you should also find that your skills in understanding complex mathematical texts are improving.

You should now be able to:

- use the definition of derivative to show that a given function is or is not differentiable at a point

- use the Cauchy–Riemann equations to show that a function is or 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

- appreciate how complex integrals can be defined by analogy with real integrals

- define the integral of a complex function along a contour and evaluate such integrals

- state and use several key theorems to evaluate contour integrals.

This OpenLearn course is an extract from the Open University course M337 Complex analysis.

OpenLearn - Introduction to complex analysis
Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.