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After this, students are then encouraged to take an 11th or 12th grade course in physics, which does use more advanced math, including vectors, geometry, and more involved algebra. There is a large overlap between the Physics First movement, and the movement towards teaching conceptual physics - teaching physics in a way that emphasizes a ...
Condensed versions of the full Schaum's Outlines called "Easy Outlines" started to appear in the late 1990s, aimed primarily at high-school students, especially those taking AP courses. These typically feature the same explanatory material as their full-size counterparts, sometimes edited to omit advanced topics, but contain greatly reduced ...
The left radical and right radical of the form B are the kernels of B 1 and B 2 respectively; [2] they are the vectors orthogonal to the whole space on the left and on the right. [3] If V is finite-dimensional then the rank of B 1 is equal to the rank of B 2. If this number is equal to dim(V) then B 1 and B 2 are linear isomorphisms from V to V ...
When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
In mathematics, a biorthogonal system is a pair of indexed families of vectors ~ ~ such that ~, ~ =,, where and form a pair of topological vector spaces that are in duality, , is a bilinear mapping and , is the Kronecker delta.
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
e 1, e 2, e 3 to the coordinate curves (left), dual basis, covector basis, or reciprocal basis e 1, e 2, e 3 to coordinate surfaces (right), in 3-d general curvilinear coordinates (q 1, q 2, q 3), a tuple of numbers to define a point in a position space. Note the basis and cobasis coincide only when the basis is orthonormal. [1] [specify]
For example, in wire-frame rendering, back-face culling can be used to partially address the problem of hidden-line removal, but only for closed convex geometry. Back-face culling can also be applied to flat surfaces other than polygons, for example disks, which have a constant normal vector or extended to patches where the surface normal can ...