Consider the first-order differential operators D < sub > i </ sub > to be infinitesimal operators on Euclidean space.

Consider a smooth surface S in 3-dimensional Euclidean space R < sup > 3 </ sup >.

Consider the example of moving along a curve γ ( t ) in the Euclidean plane.

Consider a smooth surface S in 3-dimensional Euclidean space.

Consider the problem of estimating the probability that a test point in N-dimensional Euclidean space belongs to a set, where we are given sample points that definitely belong to that set.

Consider the linear subspace of the n-dimensional Euclidean space R < sup > n </ sup > that is spanned by a collection of linearly independent vectors

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

In Consider Phlebas it is noted that Minds still find humans fascinating, especially their odd ability to sometimes achieve similarly advanced reasoning as their much more complex machine brains.

Consider a slightly more complex example:

Consider an open subset U of the complex plane C. Let a be an element of U, and f: U

Consider the complex Hilbert space L < sup > 2 </ sup > and the differential operator

Consider the complex Hilbert space L < sup > 2 </ sup >( R ), and the operator which multiplies a given function by x:

Consider the Gram – Schmidt process applied to the columns of the full column rank matrix, with inner product ( or for the complex case ).

A fundamental part of ` Abdul-Bahá's teachings on evolution is the belief that all life came from the same origin: " the origin of all material life is one ..." He states that from this sole origin, the complete diversity of life was generated: " Consider the world of created beings, how varied and diverse they are in species, yet with one sole origin " He explains that a slow, gradual process led to the development of complex entities:

Consider the complex logarithm function log z.

* Consider the C *- algebra of complex square matrices.

Consider for example any compact connected complex manifold M: any holomorphic function on it is locally constant by Liouville's theorem.

Consider a complex scalar field φ, with the constraint that φ < sup >*</ sup > φ = v², a constant.

Consider a complex, real-world problem, like those of marketing or making policies for a nation, where there are many governing factors, and most of them cannot be expressed as numerical time series data, as one would like to have for building mathematical models.

Consider a once-punctured elliptic curve, given as the locus D of complex points satisfying, where and is a complex number.

Consider a d < sup > 6 </ sup > octahedral complex ( example IrBr < sub > 6 </ sub >< sup > 3 -</ sup >).

* Consider C, the field of complex numbers, as a 1-dimensional vector space.

Consider a polygon in the complex plane.

Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.

Consider, for example, the implication this has for plane rotations.

Consider the plane spanned by and, where is a ket in the subspace perpendicular to.

Consider the special case in which the axis of rotation lies in the xy plane.

Consider two points A and B in two dimensional plane flow.

Consider two dimensional plane flow within a Cartesian coordinate system.

Consider a sphere B of radius 1 and a plane P touching B at the South Pole S of B.

Consider now the Minkowski plane: R < sup > 2 </ sup > equipped with the metric

* Consider a uniform layer of fluid over an infinite horizontal plane.

Consider a " small " light source located on-axis in the object plane of the lens.

Consider a plane with a compact arrangement of spheres on it.

Consider a pair of parallel lines in an affine plane A.

Consider a planar projection of each knot and suppose these projections are disjoint. Find a rectangle in the plane where one pair of sides are arcs along each knot but is otherwise disjoint from the knots.

Consider a point in a continuum under a state of plane stress, or plane strain, with stress components and all other stress components equal to zero ( Figure 7. 1, Figure 8. 1 ).

Consider a set of points R ( R is a vector depicting a point in a Bravais lattice ) constituting a Bravais lattice, and a plane wave defined by:

Consider the illustration, depicting a plane intersecting a cone to form an ellipse ( the interior of the ellipse is colored light blue ).

Consider two proof masses vibrating in plane ( as in the MEMS gyro ) at frequency.

Consider region D in the plane: a unit circle or general polygon — the asymptotics of the problem, which are the interesting aspect, aren't dependent on the exact shape.

* Consider a triangle in the plane with unequal sides.

Consider an inertial observer in Minkowski spacetime who encounters a sandwich plane wave.

Consider a plane wave where all perturbed quantities vary as exp ( i ( kx-ωt )).