Lecture 10 - Second order linear differential equations
... y 00 − y = 0 y 00 = y We are looking for a function y that is equal to its second derivative! First guess: y(t) = et . Is y a solution? 1. Does y satisfy the differential equation? Yes! y 0 (t) = et y 00 (t) = et y 00 = y 2. Does y satisfy the initial conditions? No! y(0) = 1 Improved first guess: y ...
... y 00 − y = 0 y 00 = y We are looking for a function y that is equal to its second derivative! First guess: y(t) = et . Is y a solution? 1. Does y satisfy the differential equation? Yes! y 0 (t) = et y 00 (t) = et y 00 = y 2. Does y satisfy the initial conditions? No! y(0) = 1 Improved first guess: y ...
7th Grade Math - Study Sheet for End-of
... Coordinate plane - the plane containing the x and y axes Quadrant - one of the four sections of the coordinate plane x-axis - the horizontal reference line on the coordinate plane y - axis - the vertical reference line on the coordinate plane Origin - the intersection of the x and y axes (0,0) Order ...
... Coordinate plane - the plane containing the x and y axes Quadrant - one of the four sections of the coordinate plane x-axis - the horizontal reference line on the coordinate plane y - axis - the vertical reference line on the coordinate plane Origin - the intersection of the x and y axes (0,0) Order ...
BKL singularity
A BKL (Belinsky–Khalatnikov–Lifshitz) singularity is a model of the dynamic evolution of the Universe near the initial singularity, described by an anisotropic, homogeneous, chaotic solution to Einstein's field equations of gravitation. According to this model, the Universe is oscillating (expanding and contracting) around a singular point (singularity) in which time and space become equal to zero. This singularity is physically real in the sense that it is a necessary property of the solution, and will appear also in the exact solution of those equations. The singularity is not artificially created by the assumptions and simplifications made by the other well-known special solutions such as the Friedmann–Lemaître–Robertson–Walker, quasi-isotropic, and Kasner solutions.The Mixmaster universe is a solution to general relativity that exhibits properties similar to those discussed by BKL.