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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.
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Write down the equation of the line which passes through the points (2, -1, 3) and (1, 4, -3). Write all three forms of the equation of the line. Solution To do the above
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find k,is -2 a root of the equation 3x2
lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x? Ans) all no.s are positive or 0. so limit is either positive
Standardization of Variables - Before we use the general distribution curve to determine probabilities of the continuous variables, we require standardizing the original units
Example 1: Multiply 432 by 8. Solution: 432 × 8 -------------- 3,456 In multiplying the multiplier in the units column to the multiplica
2yx+3y=30
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
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