Integral curve, the Glossary

Table of Contents

1. 33 relations: Autonomous system (mathematics), Banach manifold, Bundle map, Canonical form, Cartesian coordinate system, Dynamical system, Dynamical systems theory, Electric field, Field line, Flow velocity, Fluid, Fréchet derivative, Function composition, Induced homomorphism, Interval (mathematics), Lipschitz continuity, Magnetic field, Mathematics, Number line, Open set, Orbit (dynamics), Ordinary differential equation, Parametric equation, Physics, Picard–Lindelöf theorem, Projection (mathematics), Slope field, Streamlines, streaklines, and pathlines, Tangent, Tangent bundle, Trajectory, Vector field, Vector-valued function.

Autonomous system (mathematics)

In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. Integral curve and autonomous system (mathematics) are ordinary differential equations.

See Integral curve and Autonomous system (mathematics)

Banach manifold

In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Integral curve and Banach manifold are differential geometry.

See Integral curve and Banach manifold

Bundle map

In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles.

See Integral curve and Bundle map

Canonical form

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

See Integral curve and Canonical form

Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See Integral curve and Cartesian coordinate system

Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve.

See Integral curve and Dynamical system

Dynamical systems theory

Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations.

See Integral curve and Dynamical systems theory

Electric field

An electric field (sometimes called E-field) is the physical field that surrounds electrically charged particles.

See Integral curve and Electric field

Field line

A field line is a graphical visual aid for visualizing vector fields.

See Integral curve and Field line

Flow velocity

In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum.

See Integral curve and Flow velocity

Fluid

In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force.

See Integral curve and Fluid

Fréchet derivative

In mathematics, the Fréchet derivative is a derivative defined on normed spaces.

See Integral curve and Fréchet derivative

Function composition

In mathematics, function composition is an operation that takes two functions and, and produces a function such that.

See Integral curve and Function composition

Induced homomorphism

In mathematics, especially in algebraic topology, an induced homomorphism is a homomorphism derived in a canonical way from another map.

See Integral curve and Induced homomorphism

Interval (mathematics)

In mathematics, a (real) interval is the set of all real numbers lying between two fixed endpoints with no "gaps".

See Integral curve and Interval (mathematics)

Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions.

See Integral curve and Lipschitz continuity

Magnetic field

A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

See Integral curve and Magnetic field

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Integral curve and Mathematics

Number line

In elementary mathematics, a number line is a picture of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.

See Integral curve and Number line

Open set

In mathematics, an open set is a generalization of an open interval in the real line.

See Integral curve and Open set

Orbit (dynamics)

In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system.

See Integral curve and Orbit (dynamics)

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. Integral curve and ordinary differential equation are ordinary differential equations.

See Integral curve and Ordinary differential equation

Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

See Integral curve and Parametric equation

Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

See Integral curve and Physics

Picard–Lindelöf theorem

In mathematics, specifically the study of differential equations, the Picard–Lindelöf theorem gives a set of conditions under which an initial value problem has a unique solution. Integral curve and Picard–Lindelöf theorem are ordinary differential equations.

See Integral curve and Picard–Lindelöf theorem

Projection (mathematics)

In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure).

See Integral curve and Projection (mathematics)

Slope field

A slope field (also called a direction field) is a graphical representation of the solutions to a first-order differential equation of a scalar function.

See Integral curve and Slope field

Streamlines, streaklines, and pathlines

Streamlines, streaklines and pathlines are field lines in a fluid flow.

See Integral curve and Streamlines, streaklines, and pathlines

Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Integral curve and tangent are differential geometry.

See Integral curve and Tangent

Tangent bundle

A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself.

See Integral curve and Tangent bundle

Trajectory

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time.

See Integral curve and Trajectory

Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n.

See Integral curve and Vector field

Vector-valued function

A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.

See Integral curve and Vector-valued function

References

[1] https://en.wikipedia.org/wiki/Integral_curve

Also known as Integral curve of a vector field, Integral surface, Solution curve.