Lectures related to Exterior algebra

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Introduces the concept of differential forms and their applications in n-dimensional manifolds, including the Levi-Civita tensor and volume form.

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Explores the change of variables formula in higher dimensions and its application through determinant algebra and a practical example.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Explores rectilinear movement, vector algebra, scalar products, and vector decomposition in a three-dimensional space.

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Explores the scalar product of vectors, including properties and calculation methods.

Explores the change of variables formula in higher dimensions and its application through an example.

Explores Lyapunov functions, Chetaev's theorem, and differential forms classification.

Covers the concepts of the hyperbola and ellipse in analytical geometry.

Introduces multilinear forms in linear algebra, emphasizing clarity and logic in presentation.

Covers the decomposition of vectors into scalar and vector products.

Explores the derivative of a product of functions and discusses algebraic products and scalar products of functions.

Covers the vector product and its geometric interpretation in a Cartesian coordinate system.

Covers geometric places, symmetry, alignment, circles, radii, diameters, and more in a plane.

Explores multilinear forms in linear algebra, emphasizing their role in vector space transformations.