Surface Integrals and Parametrization

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Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Understanding Jacobian and Normal Vectors in Surfaces

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

Advanced Analysis II: Length of Continuously Differentiable Paths

Explores the length of continuously differentiable paths using integrals and parametrizations.

Surface Integrals: Scalar Fields

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

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Green-Riemann Formula: Curvilinear Integrals

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Curve Integrals: Gauss/Green Theorem

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

Green Theorem: Analyzing Potential Derivatives

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

Regular Surfaces: Painting with Normal Vectors

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