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 ( Euclidean ) complex plane equipped with the metric

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, 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 1D situation where there is a jump in the scalar conserved physical quantity, which is governed by the hyperbolic conservation law

Consider a scalar quantity φ = φ ( x, t ), where t is understood as time and x as position.

Consider that the scalar fields in Green's second identity are the Cartesian components of vector fields, i. e. and.

Consider a bug that is moving through a volume where there is some scalar,

Consider a shear field with a height of H and a cross-sectional area of A opposed by a manometer with a height of H ( referred to the same base as H ) and a cross-sectional area of A.

Consider, for instance, particles suspended in a viscous fluid in a gravitational field.

* Consider the field K = Q ( ³ √ 2 ).

Consider the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell as in the following diagram.

Consider, for example, what happens when an object in the periphery of the visual field moves, and a person looks toward it.

" Mother Maria Marthe ( Lilia Skala, called " Mother Maria "), responds by asking him to read another Bible verse from the Sermon on the Mount: " Consider the lilies of the field, how they grow ; they toil not, neither do they spin.

Consider the following commutative diagram in any abelian category ( such as the category of abelian groups or the category of vector spaces over a given field ) or in the category of groups.

Consider a light wave propagating along the z principal axis polarised such the electric field of the wave is parallel to the x-axis.

Consider a particle of mass, moving in a potential field.

Consider the Laplacian of the x component of the magnetic field

Consider a finite group G, a field k and the group algebra kG.

Consider a vector field v on S, that is, for each x in S, v ( x ) is a vector.

Consider the following test case: The field f has been on for infinite time and is switched off at t = 0

Consider a ( hyper ) elliptic curve over a finite field where is the power of a prime number.

Consider a hyperelliptic curve of genus over the field where is the power of a prime number and define as but now over the field.

Consider the net electric field E produced by a light wave of frequency ω together with an external electric field E < sub > 0 </ sub >:

Consider a five-frame clip of a ball moving from the bottom left of a field of vision, to the top right.

Consider a simple gravity pendulum, whose length equals the radius of the Earth, suspended in a uniform gravitational field of the same strength as that experienced at the Earth's surface.

Consider the simplified case of a vehicle with constant mass accelerating vertically upwards with a constant thrust per unit mass a in a gravitational field of strength g. The actual acceleration of the craft is a-g and it is using delta-v at a rate of a per unit time.

Consider a Lie algebra g over a field K. Every element x of g defines the adjoint endomorphism ad ( x ) ( also written as ad < sub > x </ sub >) of g with the help of the Lie bracket, as

Consider a date field, e. g. " September 19, 2004 ".

Consider two bases for elements in a finite field, GF ( p < sup > m </ sup >):