Complex Analysis Course
Master conformal mappings, residue calculus, and singularity analysis in complex analysis with practical applications to real integrals and rigorous problem-solving techniques.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This Complex Analysis Course provides a focused route to mastering conformal maps, Möbius transformations, and mapping the upper half-plane to the unit disk, then applies these tools to residue calculus, contour integration, and singularity analysis. You will practise solving real integrals, handling poles and essential singularities, and using analytic continuation, while learning clear templates and notation for rigorous, publication-ready solutions.
Elevify advantages
Develop skills
- Conformal mapping mastery: design Möbius maps from half-plane to unit disk.
- Residue calculus fluency: evaluate tough real integrals via contour methods fast.
- Singularity analysis skills: classify poles, essentials, and removable points.
- Analytic continuation tools: extend meromorphic functions across complex domains.
- Rigorous writeup techniques: present complex solutions clearly and professionally.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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