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- ...ane are equivalent in affine geometry and are equivalent in special affine geometry if their interior has the same area. We will concentrate on the equivalence ...y except in very special circumstances. It will, by the standard theory of differential equations, have a solution away from points where the velocity vanishes. We ...6 KB (1,146 words) - 07:19, 24 September 2006
- '''Differential geometry''' studies geometry by considering differentiable paramaterizations of curves, surfaces, and hi One goal of differential geometry is to classify and represent differentiable curves in ways which are indepe ...1 KB (209 words) - 21:37, 12 October 2007
- 2 KB (417 words) - 08:17, 25 November 2007
- 3 KB (561 words) - 02:11, 10 December 2007
- 864 bytes (171 words) - 01:17, 10 December 2007
Page text matches
- '''Differential geometry''' studies geometry by considering differentiable paramaterizations of curves, surfaces, and hi One goal of differential geometry is to classify and represent differentiable curves in ways which are indepe ...1 KB (209 words) - 21:37, 12 October 2007
- ...ane are equivalent in affine geometry and are equivalent in special affine geometry if their interior has the same area. We will concentrate on the equivalence ...y except in very special circumstances. It will, by the standard theory of differential equations, have a solution away from points where the velocity vanishes. We ...6 KB (1,146 words) - 07:19, 24 September 2006
- ==Differential Topology== ..." Differential topology is a sort of hybrid between algebraic topology and geometry, where distance is still irrelevant, but "smoothness" of functions and surf ...6 KB (786 words) - 12:28, 30 January 2008
- ...int set spaces but instead, the algebra of functions over them. If M is a (differential) manifold and H is an (smooth) algebra bundle over M with a Grassmann algeb ...4 KB (624 words) - 09:58, 28 May 2007
- According to basic geometry, any three points can be fit by an elipse. This means that if we have at le == Differential Orbit Correction == ...6 KB (1,052 words) - 15:37, 8 June 2007
- ...e "point mass", to begin with) by saying that it follows a geodesic of the geometry defined by <math>dS.</math> ...g classical system follows a geodesic of the geometry defined bythe action differential <math>dS,</math> which now depends on <math>n</math> spatial coordinat ...6 KB (1,037 words) - 15:06, 25 August 2008
- It follows that the differential <math>dS</math> is homogeneous (of degree 1) in the differentials <mat ...>, and of <math>dS</math> as defining a (particle-specific) spacetime geometry. By substituting <math>1/dt</math> for <math>\lambda</math> we get: ...3 KB (631 words) - 09:21, 12 December 2010
- ...cribes how matter and energy change the geometry of spacetime, this curved geometry being interpreted as the [[Wikipedia:gravitational field|gravitational fiel ...and momentum; this result arises by using the [[Wikipedia:curvature tensor|differential Bianchi identity]] to obtain ...9 KB (1,329 words) - 03:05, 28 December 2006
- [[Category:Differential Geometry]] ...4 KB (811 words) - 23:45, 25 November 2007
- This time, however, since we are in a cylindrical geometry, it makes most sense to use cylindrical coordinates to expand the Laplacian ...ence method''' attempts to solve a differential equation by estimating the differential terms with algebraic expressions. The method works best for simple geometri ...7 KB (1,192 words) - 23:21, 13 October 2007
- ...rd algebras have important applications in a variety of fields including [[geometry]] and [[theoretical physics]]. They are named for the English geometer [[Wi ===Differential geometry=== ...34 KB (5,512 words) - 09:01, 19 January 2007
- ...nd went on to develop General Relativity as a theory based on differential geometry but many of the earlier generation of physicists were unable to accept the The adoption of differential geometry as one of the foundations of relativity theory has been traced by Walter (1 ...17 KB (2,782 words) - 16:25, 19 January 2008
- Classical mechanics uses ordinary differential equations (ODEs) to describe the properties of bodies mathematically. Thus, ...methods are not specific to mechanics but are equally applicable to every differential equation. Numerical methods for solving various equations are best studied ...15 KB (2,372 words) - 12:41, 25 June 2007
- ...numbers themselves, which have been related to the rest of mathematics and geometry by a series of formulae such as linear combinations, scalar products etc. ...h as Euclid's parallel postulate required the development of a new type of geometry that could deal with curved surfaces and real and imaginary planes. At the ...29 KB (4,806 words) - 02:22, 14 August 2007
- The study of partial differential equations requires a clear definition of what kind of numbers are being dea ...gh introduction to Euclidean space isn't very fitting in a text on Partial Differential equations, it is included so that one can see how a familiar vector space c ...16 KB (2,734 words) - 02:35, 3 December 2007
- or in differential form Differential continuity equation ...18 KB (2,940 words) - 15:56, 16 November 2007
- ...nitial (ingoing) states at infinity. The key notions in this area are the differential and the total scattering cross-section. ...such notions as Legendre transformation, Poisson brackets, and symplectic geometry. The most important application of the Hamiltonian formalism is in quantum ...9 KB (1,395 words) - 08:19, 23 June 2006
- *Differential calculus: ...on of space are embedded in the content. The treatment of formal Euclidean geometry is staged through the grades so as to assist in the gradual development of ...46 KB (6,980 words) - 14:23, 21 July 2006
- ===== Geometry ===== ...i''' direction. Similarly, '''u'''·'''∇''' is the the partial differential in the '''u''' direction, multiplied by |'''u'''| ...52 KB (8,886 words) - 22:13, 8 March 2008
- ...= -1</math> and ''L(m)'' is just a rotation in the [[wikipedia: Euclidean geometry | euclidian]] space with no real valued eigenvectors. === The geometry of space-time === ...63 KB (10,825 words) - 17:54, 12 December 2007