Complex Analysis Course
Master complex analysis with tools you can use: conformal maps, residue calculus, and analytic continuation. Learn to map domains, evaluate tough real integrals, solve Laplace and Dirichlet problems, and present rigorous results with confidence.

4 to 360 hours of flexible workload
valid certificate in your country
What Will I Learn?
This Complex Analysis Course offers a focused path 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 practice solving real integrals, handling poles and essential singularities, and using analytic continuation, while learning clear templates and notation for rigorous, publication-ready solutions.
Elevify Differentials
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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