Lectures related to Surface Orientation: Parameterization and Edge Configuration

Explains the parametric equations of surfaces of revolution generated by curves in space.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Surface Orientation: Canonical Edge and Parametrization

Explains canonical surface edge orientation and parametrization using cylindrical coordinates.

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Surface Integrals: Implicit Surfaces

Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.

Rotating Vectors in Physics 1

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Introduction to Rhino Surfaces and Meshes

Introduces working with surfaces, polysurfaces, and solids in Rhino, covering rendering, material editing, and mesh creation.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Understanding Jacobian and Normal Vectors in Surfaces

Clarifies the use of Jacobian, normal vectors in surfaces, and arccos(z) constraints.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.