Differential Geometry Course
Master curves, surfaces, and curvature with a rigorous Differential Geometry Course that links vector calculus to Gaussian and mean curvature, Frenet–Serret frames, and intuitive physics, building tools for research in mathematics and theoretical physics.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This Differential Geometry Course gives you a fast, rigorous path from vector calculus foundations to the geometry of curves and surfaces. You will work with parametrized curves, Frenet–Serret frames, and curvature and torsion, then move to first and second fundamental forms, normal vectors, and Gaussian and mean curvature, finishing with focused applications that connect these tools to core ideas in modern physics and general relativity.
Elevify advantages
Develop skills
- Compute curvature, torsion, and Frenet frames for space curves with confidence.
- Analyze first and second fundamental forms to extract key surface curvatures.
- Use cylinders and helices as quick models for intrinsic and extrinsic geometry.
- Connect geometric curvature to physical intuition in general relativity and mechanics.
- Perform fast symbolic vector calculus for parametrized 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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