Green Theorem Proof

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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.