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We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a physical situation. Mostly all of the differential equations which you will use in your job as for the engineers out there in the audience are there since somebody, at several time, modeled a situation to come up along with the differential equation which you are using.
In this section is not intended to wholly teach you how to go regarding to modeling all physical situations. A complete course could be dedicated to the subject of modeling and even not cover everything! This section is implemented to introduce you to the method of modeling and demonstrate you what is included in modeling. We will seem three different situations in this section as: Falling Bodies, Population Problems and Mixing Problems.
In these all of situations we will be forced to create assumptions that do not correctly depict reality in most cases, but without them the problems would be extremely difficult and beyond the scope of such discussion and also the course in most cases to be truthful.
Example of inflection point Determine the points of inflection on the curve of the function y = x 3 Solution The only possible inflexion points will happen where
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Standard form of the line Let's begin this section off along a quick mathematical definition of a line. Any equation that can be written in the following form,
You plan to retire when you are 65th years old. You are now 25 years old. You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6
The bowling alley suggests selecting a ball that is 1/7 of the bowlers weight. If the bowler weighs 84 pounds, how much should the bowling ball weigh?
use the distributive law to write each multiplication in a different way. then find the answer. 12x14 16x13 14x18 9x108 12x136 20x147
The length of the sides of a triangle are 2x + y/2 , 5 x/3 + y + 1/2 and 2/3 x + 2y + 5/2. If the triangle is equilateral. Find its perimeter. A ns: 2x + y/2 = 4x + y
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