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Introduction to Differential Equations

Hey, I'm teaching myself differential equations, and I'm using a rather old, but quite possibly brilliant text book printed in 1974. I've finished Algebra, and now I've been learning Advanced Mathematics and starting on the topic of Differential Equations.

It states that I should consider the following statements

i) The tangent to a certain graph at every point P is at right-angles to the line OP

ii) The rate at which a rumour is spreading through the school depends on the number of people who have heard it already.

Is this vital? The second question seems almost like a branch of theoretical probability. Also, what is a derivative? I've read the rules for the gradient of perpendicular lines and they seem very similar to that of the rules of the gradient found in Algebra.

Correct me if I'm wrong but do these equations calculate the length a curve in a graph, as oppose the calculating the area or circumference within the realm of Algebra?

Can someone please tell me what are differential equations, what are they used for and why are they so important? Also, I have problems with normal functions, as I have not practiced them much, but I'm rather good at trigonometric functions using the unit circle. Will this help?

All comments are very much appreciated. Many thanks to all! I appologise for all the questions, but I'm rather excited learning such things.
Reply 1
Avatar for _Ravi_
_Ravi_
10
You may find these videos useful

http://www.khanacademy.org/
Reply 2
Avatar for nick198929
nick198929
OP
1
Thanks, Ravi :smile: All other comments are very much appreciated :smile:
Reply 3
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nick198929
OP
1
Can someone please post their comments? Thank you :smile:
Reply 4
Avatar for around
around
13
Differential equations govern the change of a system based on the rates of change of variables in the system. So for your second example, the rate at which the rumour is spreading (ie the rate of change of the number of people who have heard the rumour) is a function of the people who have heard the rumour. And yes, for small numbers of people, you can't really use the machinery of differential equations, but if you have enough people, and take a long term view of it, you can model the spread of the rumour as a smooth process.

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