Problem set 4
... Due at the beginning of class on Tuesday, August 18.
Matrix of discretized derivative
In the lecture it was mentioned that Newton’s equation ẍ = f could be written as a matrix
equation when discretized. Here you will do this for the simpler problem of the first derivative.
Given the position of a p ...
... (a) (6) Sketch the isocurves of this field. Indicate the direction of the gradient
(b) (7) Use linear approximation around point (1, 1) to estimate f(1.1, 1.05).
2. (7) Use either suffix notation or vector algebra (whichever you prefer) to get
rid of cross products in expression (b a ) a c ...
In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.