Cartesian form and definition via ordered pairs[ edit ] A complex number can thus be identified with an ordered pair Re zIm z in the Cartesian plane, an identification sometimes known as the Cartesian form of z. In fact, a complex number can be defined as an ordered pair a, bbut then rules for addition and multiplication must also be included as part of the definition see below. Complex plane Figure 1:

Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

We are going to give several forms of the heat equation for reference purposes, but we will only be really solving one of them. Note that with this assumption the actual shape of the cross section i.

Note that the 1-D assumption is actually not all that bad of an assumption as it might seem at first glance. If we assume that the lateral surface of the bar is perfectly insulated i. This means that heat can only flow from left to right or right to left and thus creating a 1-D temperature distribution.

The assumption of the lateral surfaces being perfectly insulated is of course impossible, but it is possible to put enough insulation on the lateral surfaces that there will be very little heat flow through them and so, at least for a time, we can consider the lateral surfaces to be perfectly insulated.

As indicated we are going to assume, at least initially, that the specific heat may not be uniform throughout the bar. Note as well that in practice the specific heat depends upon the temperature.

As noted the thermal conductivity can vary with the location in the bar. Also, much like the specific heat the thermal conductivity can vary with temperature, but we will assume that the total temperature change is not so great that this will be an issue and so we will assume for the purposes here that the thermal conductivity will not vary with temperature.

First, we know that if the temperature in a region is constant, i. Next, we know that if there is a temperature difference in a region we know the heat will flow from the hot portion to the cold portion of the region.

For example, if it is hotter to the right then we know that the heat should flow to the left. Finally, the greater the temperature difference in a region i.

In this case we generally say that the material in the bar is uniform. There are four of them that are fairly common boundary conditions. The first type of boundary conditions that we can have would be the prescribed temperature boundary conditions, also called Dirichlet conditions.

These are usually used when the bar is in a moving fluid and note we can consider air to be a fluid for this purpose. Here are the equations for this kind of boundary condition. Note that the two conditions do vary slightly depending on which boundary we are at.How to find an equation given the absolute value graph?

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So the equation of the left line is $\color{blue}{y=a(1-x) -4}$ and the right line has equation $\color{red}{y=a(x-1) -4}$. How to find equation for a line on a graph.

1. Find a function from graph.

0. Reduce a given linear equation in two variables to the standard form y = mx + c; calculate gradients and intercepts of the graphs and then plot them to check.

Want to write an equation to translate the graph of an absolute value equation? This tutorial takes you through that process step-by-step! Take an absolute value equation and perform a vertical and horizontal translation to create a new equation.

The equation of time describes the discrepancy between two kinds of solar urbanagricultureinitiative.com word equation is used in the medieval sense of "reconcile a difference".

The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with noons 24 hours apart.

Apparent solar time can be obtained by. In this overview, we will start with graphing straight lines, and then progress to other graphs. The only major difference, really, is in how many points you need to plot in order to draw a good graph.

In this section we will derive the vector and scalar equation of a plane. We also show how to write the equation of a plane from three points that lie in the plane.

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Calculus II - Equations of Planes