Complex Analysis Course
This course equips learners with essential tools in complex analysis, focusing on conformal mappings, residue calculus, and singularity analysis to solve advanced integrals and extend functions rigorously.

flexible workload from 4 to 360h
valid certificate in your country
What will I learn?
This Complex Analysis Course provides a focused way to master conformal maps, Möbius transformations, and mapping the upper half-plane to the unit disk, then uses these tools for residue calculus, contour integration, and singularity analysis. You will practise solving real integrals, dealing with poles and essential singularities, and applying 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 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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