Lectures related to Parametrization by Arc Length

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Osculating Planes and Parameterized Curves

Covers the concept of osculating planes and parameterized curves, discussing the speed of points and linear independence.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

Continuity Definition: Epsilon and Delta MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

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

Definition of Indefinite Integral MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Explains the definition and properties of indefinite integrals, highlighting the relationship between primitives and the set of all primitives of a function.

Limit in a Point: Definition and Examples

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

Developpements limités MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Derivatives and Functions: Definitions and Interpretations Log in to Mediaspace to watch this video

Covers the definition of derivative functions and their interpretation, focusing on differentiability, velocity, and curve lengths.

Advanced Analysis II: Length of Continuously Differentiable Paths Log in to Mediaspace to watch this video

Explores the length of continuously differentiable paths using integrals and parametrizations.

Differential Calculus: Definition and Derivability Log in to Mediaspace to watch this video

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

Parametrization of Straight Lines Log in to Mediaspace to watch this video

Covers the parametrization of straight lines and their geometric interpretation.

Differentiable Functions and Lagrange Multipliers Log in to Mediaspace to watch this video

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Vector Calculus: Line Integrals Log in to Mediaspace to watch this video

Covers the concept of line integrals and their application in vector fields.

Analyse II: Directional Derivative Log in to Mediaspace to watch this video

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

Advanced Analysis II: Tangent Plan and Differentiability Log in to Mediaspace to watch this video

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.