Lectures related to Parametrization by Arc Length

Derivatives and Functions: Definitions and Interpretations

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

Gaussian Curvature and Geodesics

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

Advanced Analysis II: Length of Continuously Differentiable Paths

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

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.

Differential Calculus: Definition and Derivability

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

Parametrization of Straight Lines

Covers the parametrization of straight lines and their geometric interpretation.

Differentiable Functions and Lagrange Multipliers

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

Vector Calculus: Line Integrals

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

Analyse II: Directional Derivative

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

Advanced Analysis II: Tangent Plan and Differentiability

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

Topology of Riemann Surfaces

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

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Partial Derivatives: Higher Order and Applications

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

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Differentiability of Functions of Several Variables

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Osculating Planes and Parameterized Curves

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

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Differentiable Functions: Definitions and Properties

Covers the definition and properties of differentiable functions, focusing on differentiability, limits, continuity, and partial derivatives.