StewartCalc7e_16_07
... If it is possible to choose a unit normal vector n at every such point (x, y, z) so that n varies continuously over S, then S is called an oriented surface and the given choice of n provides S with an orientation. There are two possible orientations for any orientable surface (see Figure 7). ...
... If it is possible to choose a unit normal vector n at every such point (x, y, z) so that n varies continuously over S, then S is called an oriented surface and the given choice of n provides S with an orientation. There are two possible orientations for any orientable surface (see Figure 7). ...
Systems of Particles
... frictionless horizontal tract. While the cart is at rest, the ball is given an initial velocity v0 2 gl . ...
... frictionless horizontal tract. While the cart is at rest, the ball is given an initial velocity v0 2 gl . ...
Synthetic electromagnetic fields for ultracold atoms
... where E1 and E2 are the eigenenergies of the ground and the excited state. The probability that the atom occupies a certain state equals |c1 |2 for the ground and |c2 |2 for the excited state, |c1 |2 +|c2 |2 = 1. We assume that the majority of the atomic population is in the ground state in the begi ...
... where E1 and E2 are the eigenenergies of the ground and the excited state. The probability that the atom occupies a certain state equals |c1 |2 for the ground and |c2 |2 for the excited state, |c1 |2 +|c2 |2 = 1. We assume that the majority of the atomic population is in the ground state in the begi ...
The weak dual topology
... Definition. Let X be a normed vector space over K(= R, C). For every x ∈ X, let x : X∗ → K be the linear map defined by x (φ) = φ(x), ∀ φ ∈ X∗ . We equipp the vector space X∗ with the weak topology defined by the family Ξ = (x )x∈X . This topology is called the weak dual topology, which is denote ...
... Definition. Let X be a normed vector space over K(= R, C). For every x ∈ X, let x : X∗ → K be the linear map defined by x (φ) = φ(x), ∀ φ ∈ X∗ . We equipp the vector space X∗ with the weak topology defined by the family Ξ = (x )x∈X . This topology is called the weak dual topology, which is denote ...
M1GLA: Geometry and Linear Algebra Lecture Notes
... ||x − y|| = (x1 − y1 )2 + (x2 − y2 )2 Definition (Scalar product). The scalar product (or dot product) of two vectors x, y ∈ R2 is (x · y) = x1 y1 + x2 y2 E.g. If x = (1, −1), y = (1, 2) then (x · y) = 1 + (−2) = −1. Easy properties: For any vectors x, y, z ∈ R2 • x · (y + z) = x · y + x · z (distri ...
... ||x − y|| = (x1 − y1 )2 + (x2 − y2 )2 Definition (Scalar product). The scalar product (or dot product) of two vectors x, y ∈ R2 is (x · y) = x1 y1 + x2 y2 E.g. If x = (1, −1), y = (1, 2) then (x · y) = 1 + (−2) = −1. Easy properties: For any vectors x, y, z ∈ R2 • x · (y + z) = x · y + x · z (distri ...