Lectures related to Differential of a Morphism

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

Covers strategies for matrix operations and the concept of vector spaces.

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

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

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explores the differential of group actions on vector spaces and the behavior of orbit maps.

Explores the Gauss representation of complex numbers, focusing on addition, multiplication, bases, and vector space dimensions.

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Covers various examples and general concepts related to linear applications in algebra.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.