Complex Analysis Course
This course builds strong skills in complex analysis, covering conformal maps, Möbius transformations, residue calculus, contour integration, singularity classification, and analytic continuation. Learners will solve challenging real integrals, handle various singularities, map complex domains effectively, and produce professional, publication-quality solutions with clear notation and structured approaches.

flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Gain expertise in conformal mappings, Möbius transformations, and mapping upper half-plane to unit disk, applying them to residue calculus, contour integration, and singularity analysis. Master solving real integrals, managing poles and essential singularities, analytic continuation, with templates for rigorous solutions.
Elevify advantages
Develop skills
- Master conformal mappings: create Möbius transformations mapping half-plane to unit disk.
- Achieve fluency in residue calculus: compute difficult real integrals using contours swiftly.
- Develop singularity analysis: identify poles, essential singularities, and removable points accurately.
- Learn analytic continuation: extend meromorphic functions over complex regions.
- Perfect rigorous presentation: write clear, professional solutions for complex problems.
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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