Diff. Geometry·Course
Differential Geometry
Differential geometry: curves and surfaces, curvature, geodesics, tensor calculus, and manifolds
6
Modules
18
Articles
~2 h
Reading
IV
CLOs
§ 01 — Curriculum
6 modules.
Each module is a small unit. Most read in sequence — but a determined reader can begin anywhere.
- M ITheory of CurvesFrenet frame, curvature and torsion, natural equations of a curve3 articles
18 minBegin → - M IITheory of SurfacesFirst and second fundamental forms, Gaussian and mean curvature3 articles
18 minBegin → - M IIISmooth ManifoldsCharts, tangent space, vector fields3 articles
18 minBegin → - M IVDifferential Forms and Stokes’ TheoremWedge product, exterior derivative, generalized Stokes’ theorem3 articles
18 minBegin → - M VTopological SpacesTopological spaces, connectedness, compactness3 articles
18 minBegin → - M VIFundamental Group and CoveringsLoops, fundamental group, covering space theory3 articles
18 minBegin →
§ 02 — Learning outcomes
4 outcomes.
CLO I
Theory of Curves
Compute curvature and torsion of curves and understand the Frenet–Serret formulas
CLO II
Theory of Surfaces
Study the first and second fundamental forms and Gaussian curvature
CLO III
Geodesics
Determine geodesics on surfaces and understand parallel transport
CLO IV
Manifolds
Understand the basics of differentiable manifolds and tensor analysis
§ 03 — Practices