This free course, Introduction to complex analysis, is an extract from the third level Open University course M337 Complex analysis, which develops the theory of functions of a complex variable, emphasising their geometric properties and indicating some applications.
Introduction to complex analysis consists of two sessions. The first session covers differentiation, and the second session covers integration of complex functions. The course should take about 12 hours to study.
This course forms part of the Dangoor Education course collection, the educational arm of The Exilarch's Foundation.
Course learning outcomes
After studying this course, you should 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.
First Published: 28/03/2023
Updated: 28/03/2023