Differential Geometry Course
This comprehensive Differential Geometry course equips learners with essential tools for analysing curves, surfaces, and curvatures. Starting from vector calculus principles, it covers Frenet-Serret frames, fundamental forms, Gaussian and mean curvatures, and their vital applications in modern physics and general relativity, ideal for aspiring mathematicians and physicists.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain a swift, solid foundation in differential geometry, progressing from vector calculus basics to the study of curves and surfaces. Master parametrized curves, Frenet-Serret frames, curvature, torsion, first and second fundamental forms, normal vectors, Gaussian and mean curvature, with key links to 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 surface curvatures.
- Apply cylinders and helices to model intrinsic and extrinsic geometry.
- Link geometric curvature concepts to physics in relativity and mechanics.
- Execute efficient symbolic vector calculus on 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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