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...where we have a single differential equation and found several methods to aid us in finding solutions to these equations. But what happens if we have two == First order systems == ...

The remainder of this section discusses suggests fractional forms that aid in separation, since the actual method and theory hold. ...

In the first method presented here, you will need a ruler, or any object with evenly spa The first method we present here for estimating the width of a stream will involve ch ...

by an equals sign. An indentity however is a memory aid of a mathematical ...

#Use the summation notation to represent the expression in the first example. (Note:I suggest getting a visual aid on this one:showing that you can sum a two dimensional array in either dire ...

...r Credits. All other accounts are the reverse. First memorize the acronyms AID (Assets Increase Decrease) & EID (Expenses Increase Decrease)and then keep ...

##Cmpute <math>T</math>, using your spacetime diagram as an aid. ...ess than the speed of light is the electron traveling? Hint: It is best to first develop an approximation for the relationship between <math>\gamma = (1 - v ...

...for many topological spaces the similarities are remote, but nevertheless aid in judgment and guide proofs. Interesting differences in the structure of ...

...tion on the curve. Substitutions can be performed before rearrangement (to aid in factorisation) if the value is required, and not the expression. First, we need to examine the equation relating height to volume. Assuming that t ...

...be refilled repeatedly with different solutions. It will have to be rinsed first with distilled water, then rinsed with a small amount of the solution to be ...ce you measure is the systematic error between the two cuvettes, using the first cuvette as the blank. This absorbance will be subtracted from all future sa ...

...vector''', or solution, is the vector drawn from the initial point of the first vector to the terminal point of the second vector when they are drawn tip-t To determine the projection we first note that <math>\mathbf{pr_v}\mathbf{u}</math> is proportional to <math>\ma ...

One useful application of derivatives is as an aid in the calculation of '''related rates'''. What is a related rate? In each ...s able to develop his Second Law of Motion. Let's play around with them. First, we know that velocity is the derivative of the location function, and acce ...

...oxygenated blood to the rest of the body. When a person performs CPR, the first task is to artificially fill the lungs with oxygen. This is done by rescue [[Category:First aid]] ...

The first sign of trouble is square roots. Famously, <math>\sqrt{2}</math> is not ra ...relations on <math>\mathbb R</math>, we need to introduce more notation to aid in talking about them. Hopefully all these conventions should be familiar ...

The discovery of the electron was the first indication that the atom had internal structure. This structure was initial less hassle. The thing to remember is that it is only a model, an aid to understanding. Atoms are not really little solar systems. ...

...em process. The plant is the preexisting system that does not (without the aid of a controller or a compensator) meet the given specifications. Plants are ...a certain building with 5 floors. Pressing button "1" will take you to the first floor, and pressing button "5" will take you to the fifth floor, etc. For r ...

...t hospital physicians to request blood cultures. Identifying the agent may aid in choosing the correct antibiotic and addressing particular risk factors. ...

...put on a reference substance, which deflected the spring by 5 inches. The first rock made the water in a certain graduated cylinder rise by 20 mm, and the ...cond fluid is the exact same as the force holding up the hydrometer in the first fluid, i.e <math>mg</math> ...

...readsheet has a number of parts that you should be familiar with. When you first open up the spreadsheet program, you will see something that looks like thi First off, notice that the entire page is split up into boxes, and each one is la ...

...le-operation process. Therefore, several techniques have been developed to aid engineers in their analyses. This section describes these techniques and ho First we have to relate the velocity and area given to us to the mass flowrate of ...