Green's Theorem: Surface Integrals

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Differential Geometry: Parametric Curves & Surfaces

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

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Surface Integrals: Orientation and Computation

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

Shells I

Covers linear pressure vessels, thin shells, and critical buckling pressure, emphasizing the dimensional reduction from 3D to 2D.

Green's Theorem: Demonstration and Applications

Covers the demonstration and applications of Green's Theorem in vector fields.

Surface Integrals and Parametrization

Explores the analogy between curves and surfaces, emphasizing the importance of choosing parameters for normal vectors.

Green's Theorem: Applications

Covers the application of Green's Theorem in analyzing vector fields and calculating line integrals.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

Geometrical Aspects of Differential Operators

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

Divergence and Stokes' Theorems

Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.