MATH-123(b): Geometry

Lectures in this course (35)

Covers equations and parametrizations of planes, and the formula for rotations.

Covers the preservation of isometry by rotations and symmetries.

Covers basic notions of vector geometry, including scalar product, norm, and projection.

Covers affine subspaces, lines, planes, intersections, cross product, and distance calculations in vectorial geometry.

Explores the concept of curve length and its geometric properties.

Explains the curvature oriented change of notes in OneNote for Windows 10.

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

Explains vector fields, Frenet frame, and local curve behavior using Frenet-Serret formulas.

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Covers the TNB frame and Frenet-Serret formulas for understanding curve behavior.

Explores stereographic projection and sphere parameterization, emphasizing regularity and line independence.

Covers the concept of parameterized surfaces in 3D space with examples like cylinders and spheres.

Explores the definition and applications of tangent vectors in determining curve directions on surfaces.

Explores isometries, distinguishing between rotations and reflections, and the preservation of orientation in geometric transformations.

Explains surface normals for parametric and implicit surfaces, focusing on vector analysis and examples with spheres.

Explains regular points on implicit surfaces and their relationship with gradients and tangent planes.

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Explores geodesics and surface area calculation for rotationally symmetric surfaces.

Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.

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