Differential Geometry Course
Gain mastery over curves, surfaces, and curvature through this rigorous Differential Geometry course. It bridges vector calculus to Gaussian and mean curvature, Frenet-Serret frames, and physics insights, equipping you with essential tools for advanced research in mathematics and theoretical physics.

from 4 to 360h flexible workload
certificate valid in your country
What will I learn?
This course provides a swift, rigorous journey from vector calculus basics to the geometry of curves and surfaces. Learners handle parametrized curves, Frenet-Serret frames, curvature and torsion, then advance to first and second fundamental forms, normal vectors, Gaussian and mean curvature, ending with key applications linking to modern physics and general relativity.
Elevify advantages
Develop skills
- Compute curvature, torsion, and Frenet frames for space curves confidently.
- Analyze first and second fundamental forms to determine key surface curvatures.
- Apply cylinders and helices as models for intrinsic and extrinsic geometry.
- Link geometric curvature to physical concepts in general relativity and mechanics.
- Execute efficient symbolic vector calculus for curves and surfaces.
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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