^{n}} that is r-times continuously differentiable (that is, the component functions of γ are continuously differentiable), where n ∈ N {\displaystyle n\in...

properties. Roughly speaking a differentiable curve is a curve that is defined as being locally the image of an injective differentiable function γ : I → X {\displaystyle...

at a point of a differentiable curve is the curvature of its osculating circle — that is, the circle that best approximates the curve near this point...

another is differentiable), then computations done in one chart are valid in any other differentiable chart. In formal terms, a differentiable manifold...

as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also...

C^{1}} consists of all differentiable functions whose derivative is continuous; such functions are called continuously differentiable. Thus, a C 1 {\displaystyle...

the curve with respect to time. Thus the length of a continuously differentiable curve ( x ( t ) , y ( t ) ) {\displaystyle (x(t),y(t))} , for a ≤ t ≤ b...

than just the real line. If φ : U ⊆ Rn → R is a differentiable function and γ a differentiable curve in U which starts at a point p and ends at a point...

_{2}:(-1,1)\to \mathbb {R} ^{n}} are differentiable in the ordinary sense (we call these differentiable curves initialized at x {\displaystyle x} )....

Space-filling curves are special cases of fractal curves. No differentiable space-filling curve can exist. Roughly speaking, differentiability puts a bound...

generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of...

of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean...

of the curve (with respect to motion down the curve). In differential geometry, parametric equations are usually assumed to be differentiable (or at least...

{\displaystyle (x-a)p'_{x}(a,b)+(y-b)p'_{y}(a,b)=0} , like for every differentiable curve defined by an implicit equation. In the case of polynomials, another...

along a differentiable curve in three-dimensional Euclidean space R 3 , {\displaystyle \mathbb {R} ^{3},} or the geometric properties of the curve itself...

Jacobian matrix is not maximal. It extends further to differentiable maps between differentiable manifolds, as the points where the rank of the Jacobian...

{\displaystyle M} be a differentiable manifold and let A ( M ) {\displaystyle A(M)} be the algebra of real-valued differentiable functions on M {\displaystyle...

function that is continuous everywhere but differentiable nowhere. It is also an example of a fractal curve. The Weierstrass function has historically...

the Lorenz curve is differentiable: d L ( F ) d F = x ( F ) μ {\displaystyle {\frac {dL(F)}{dF}}={\frac {x(F)}{\mu }}} If the Lorenz curve is twice differentiable...

}}(t)\right)\,dt} of a differentiable curve γ: [a, b] → M in M is invariant under positively oriented reparametrizations. A constant speed curve γ is a geodesic...

is necessary that the individual members of the family of curves are differentiable curves as the concept of tangency does not apply otherwise, and there...

speaking, the curves must be differentiable curves in the Euclidean plane. The fixed curve is kept invariant; the rolling curve is subjected to a continuous...

continuous) and P {\displaystyle P} is a differentiable path (i.e., it can be parameterized by a differentiable function) in U {\displaystyle U} with an...

functions are differentiable; Whether indifference curves are primitive or derivable from utility functions; and Whether indifference curves are convex....

and differentiable nowhere. List of fractals by Hausdorff dimension Gabriel's Horn (infinite surface area but encloses a finite volume) Gosper curve (also...

badly behaved curves, which include nowhere differentiable curves, such as the Koch snowflake and other fractal curves, or even a Jordan curve of positive...

associated infinitesimal connection in E as follows. Let γ be a differentiable curve in M with initial point γ(0) and initial tangent vector X = γ′(0)...

In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto...

Bibcode:2015arXiv150107626G Gibson, C. G. (2001), Elementary Geometry of Differentiable Curves: An Undergraduate Introduction, Cambridge University Press, ISBN 9780521011075...

other being differentiation. Integration was initially used to solve problems in mathematics and physics, such as finding the area under a curve, or determining...