Lectures related to Surface Orientation: Canonical Edge and Parametrization

Surface Integrals: Regular Parametrization

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

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.

Surface Orientation: Parameterization and Edge Configuration

Covers the parameterization of surfaces and the orientation of surface edges, emphasizing the importance of selecting the appropriate orientation and configuration.

Differential Forms Integration

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

Surface of Revolution

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

Surface Integrals: Scalar Fields

Covers the concept of surface integrals for scalar fields, focusing on regular, orientable surfaces in 3D space.

Green's Theorem: Surface Integrals

Explores Green's Theorem applied to surface integrals, emphasizing regular surfaces and coordinate transformations.

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: Parameterized Surfaces

Explores surface integrals over parameterized orientable surfaces and their applications in flux and work evaluation.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Rotating Vectors in Physics 1

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

Angle Calculation on Regular Surfaces

Covers the calculation of angles between curves on regular surfaces and the concept of curvilinear abscissa.

Understanding Jacobian and Normal Vectors in Surfaces

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

Regular Surfaces: Painting with Normal Vectors

Explores regular surfaces and painting with normal vectors, integral calculations, symmetries, and surface orientation.

Coordinate Systems: Polar, Cylindrical, Spherical

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

Surface Integrals: Implicit Surfaces

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

Surface Integrals: Orientation and Computation

Explores orientable surfaces, scalar field integrals, and practical applications through examples with a sphere and a cone.

Vector Calculus: Line Integrals

Covers the concept of line integrals and their application in vector fields.

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

Differential Geometry of Surfaces

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