3 Boundary and Initial Conditions.

Which component of the electric field intensity is always continuous at the boundary? Explanation: At the boundary of the dielectric-dielectric, the tangential component of the electric field intensity is always continuous.

In most physical problems these are boundary conditions, that describes how the system behaves on its boundaries (for all times) and initial conditions, that specify the state of the system for an initial time t=0. In the ODE problem discussed before we have two initial conditions (velocity and position at time t=0).

The initial value is the beginning output value, or the y-value when x = 0. The rate of change is how fast the output changes relative to the input, or, on a graph, how fast y changes relative to x. You can use initial value and rate of change to figure out all kinds of information about functions.

The initial value, or y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis.

Intercept: When x = 0, the corresponding y-value is the y-intercept. In the particular context of word problems, the y-intercept (that is, the point when x = 0) also refers to the starting value.

If one of the data points has the form (0,a) , then a is the initial value. Using a, substitute the second point into the equation f(x)=abx f ( x ) = a b x , and solve for b. If neither of the data points have the form (0,a) , substitute both points into two equations with the form f(x)=abx f ( x ) = a b x .

With the exception of horizontal lines, all linear functions have this property and thus have inverses that are also functions, Ex 1: On the grid below the linear function y = 2x – 4 is graphed along with the line y = x.

A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.