Lectures related to Theoretical definition

Covers the concept and calculation of directional derivatives in multivariable calculus.

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Explores Newton's laws of motion, fundamental forces in nature, and the unification of interactions.

Explores the concept of angles in circular trigonometry, emphasizing geometric angles and their properties.

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

Explores the derivation of Dynkin diagrams from Du Val singularities.

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.

Explores the definition of connections for smooth vector fields on manifolds.

Covers the properties and operations of convex functions.

Covers the concept of partial derivatives of higher order and their applications in various contexts.

Explores finding tangent equations and slopes through derivatives.

Covers the definition of continuity at a point using epsilon and delta.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Covers the basics of linear algebra, including rank, differentiable applications, and submersions.

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Explores inequalities, absolute value, and mathematical identities, emphasizing their importance in mathematical reasoning.

Covers the concept of limit in a point with definitions and examples.

Covers the concept of exponential functions and their change of variables.

Covers the definition and properties of plasma, including ionization and collective effects.

Covers cyclically monotone sets in optimal transport theory and their properties.