Graph Surfaces: Integration and Vector Calculus

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Related lectures (27)

Page 1 of 3

Explores surface integrals, emphasizing physical interpretation and mathematical calculations in vector fields and domains.

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.

Surface Integrals: Change of Variables

Explores surface integrals, change of variables, and properties of regular surfaces.

Surface Integrals, Divergence Theorem and Stocks' Theorem

Covers surface integrals, the divergence theorem, and Stocks' theorem through examples and analogies.

Surface Integrals: Parameterization and Divergence Theorem

Explores surface integrals using parameterization and the divergence theorem, with practical examples included.

Curve Integrals: Gauss/Green Theorem

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

Divergence and Stokes' Theorems

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

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Surface Integrals, Divergence Theorem

Covers surface integrals, divergence theorem, and regular domains in 2D and 3D.

Vectors and Tensors: Derivatives and Transformations

Explores gradient, divergence, and integral theorems in vector calculus.