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Simplicity is the ultimate sophistication.” — Leonardo da Vinci
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Sunday, 19 July 2015

Fundamentals of calculus Chapter 3: differential equations of functions involving one independent variable.


Fundamentals of calculus
Chapter 3: differential equations of functions involving one independent variable.


“Everything big is built out of smaller units; and if the smaller units fail to cooperate the bigger ones ultimately fall”

“A good learner never accepts the educative information he comes across unless he knows for sure, that there is no practical and logical way to contradict it”


Calculus as a whole evolved to support something new, a differential equation. One marvellous fact about differential equations are they don’t have any constants to describe the graphical structure they represent. In the previous article ‘chapter 2’, we saw how differentiation eliminates a constant. This fact can be taken advantage of to frame differential equations that elaborate the actual rate of change of different quantities. For example if, $z = ax^2 + bx +c$ then $\frac{dz}{dx} = 2ax + b$ and $\frac{d^2z}{dx^2} = 2a$ and $\frac{d^3z}{dx^3} = 0$.

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