Course

MATH-123(b): Geometry

Lectures in this course (35)

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.

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.

Explores geodesics as locally shortest paths and defines surface area using parametric squares.

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Explores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Explores principal curvatures and Gaussian curvature in the context of minimal surfaces, demonstrating their real-world applications.

Explores principal curvatures, mean curvature, umbilical points, main curvatures, and eigenvalues.

Explores mean and Gaussian curvature, emphasizing their calculation for different bases and surfaces.

Covers geodesics, isometries, and map projections, including the famous Mercator projection and its distortions.