Lectures related to Exterior derivative

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

Explores derivability, differentiability, known formulas, and algebraic operations on limits, with examples and counterexamples.

Explores the second Wolfe condition, guiding step sizes based on the directional derivative increase.

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

Introduces the First Wolfe condition to ensure a proportional decrease in the objective function relative to the step length.

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.

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

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

Covers advanced physics topics including definitions, rectilinear motion, vectors, and motion in three dimensions.

Explores the role of first and second derivatives in function curvature and convexity.

Covers the analysis of phase planes for linear systems and the Poincaré-Bendixson theorem.

Covers the definition of directional derivative and provides illustrative examples.

Delves into topology, homomorphism, and their practical implications on CAD software.

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

Explores properties of functions with continuous partial derivatives in open subsets of Rn.

Introduces partial derivatives in functions of several variables and their properties.

Delves into the concept of thresholds as porous elements blurring boundaries, creating new interactions and spatial sequences.

Explores differential calculation and the notion of derivative in advanced analysis II.

Explores the impact of materials and construction techniques on heat transfer in buildings.