Lectures related to Untitled | EPFL Graph Search

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

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: Parameterization and Divergence Theorem

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

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Understanding Normal Vectors in Calculus

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Green's Theorem: Understanding Rotations and Closed Paths

Explores Green's Theorem, rotations, closed paths, and integral signs.

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Surface Integrals: Change of Variables

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

Surface Integrals, Divergence Theorem

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

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Surface Integrals, Divergence Theorem and Stocks' Theorem

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

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Vector Calculus Review: Maxwell Equations

Covers a review of vector calculus and the Maxwell equations in electromagnetism.

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.

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

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Vectors and Tensors: Derivatives and Transformations

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