Differential Geometry Course
This rigorous Differential Geometry Course builds from vector calculus to advanced study of curves and surfaces, covering Frenet-Serret frames, curvature, torsion, fundamental forms, Gaussian and mean curvature, and their applications in physics and general relativity, equipping learners with essential tools for mathematical and theoretical physics research.

4 to 360h flexible workload
certificate valid in your country
What will I learn?
Explore differential geometry from vector calculus basics to curves and surfaces, mastering parametrized curves, Frenet-Serret frames, curvature, torsion, fundamental forms, normal vectors, Gaussian and mean curvature, with applications 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 to model 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 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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