Lectures related to Green Theorem Proof

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.

Understanding Normal Vectors in Calculus

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

Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

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Curve Integrals: Gauss/Green Theorem

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

Summary using nabla symbol

Covers the concept of nabla symbol, vector scalar, divergence, and cross product in 3D.

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Differential Forms Integration

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

Divergence of Vector Fields

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

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Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Stokes Theorem

Covers the Stokes theorem, extending the Green theorem to surfaces in R3 and explaining its application.

Geometrical Aspects of Differential Operators

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

Understanding Positive and Negative Orientation in Curves

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

Green's Theorem: Applications

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

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Vectorial Fields: Parametrization and Stokes' Theorem

Covers the parametrization of vectorial fields and the application of Stokes' theorem.

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Analysis of del operator on vector field

Explores the analysis of forces on a dipole moment using mathematical formulas and vector components.

Green's Theorem: Domain Analysis

Explores Green's Theorem application in domain analysis and potential functions.