Differential Geometry Course
Master curves, surfaces, and curvature through this rigorous Differential Geometry Course. It connects vector calculus to Gaussian and mean curvature, Frenet-Serret frames, and physics applications, equipping you with essential tools for research in mathematics and theoretical physics.

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