Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Field Derivation: Potential and Convexity

In course

MATH-203(b): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...

Description

This lecture covers the derivation of a field from a potential, exploring the concept of convexity and closed curves. The instructor guides through examples and exercises to verify the derivation of the field.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

David Valentin Strütt

Maria Colombo

Official source

Related concepts (32)

Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's Elements: "The [curved] line is [...] the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...

Algebraic curve

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0.

Plane curve

In mathematics, a plane curve is a curve in a plane that may be either a Euclidean plane, an affine plane or a projective plane. The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. Plane curves also include the Jordan curves (curves that enclose a region of the plane but need not be smooth) and the graphs of continuous functions. A plane curve can often be represented in Cartesian coordinates by an implicit equation of the form for some specific function f.

Electric potential

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work energy needed per unit of electric charge to move this charge from a reference point to the specific point in an electric field. More precisely, it is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible.

Differentiable curve

Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.

Related lectures (51)

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Analysis III: Third Class

Covers the correction of the simple curve definition and the importance of orientation in mathematical analysis.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Algebraic Curves: Normalization