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Calculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.There are two main branches of calculus.
The first is differentiation (or derivatives), which helps us to find a rate of change of one quantity compared to another.
The second is integration, which is the reverse of differentiation. We may be given a rate of change and we need to work backwards to find the original relationship (or equation) between the two quantities.
Pre-Requisites before Studying Calculus:
- Know the basic properties of polynomials (factoring and roots),
- properties of the trigonometric functions including trigonometric identities, and properties of graphs. Ie., if you know the graph of y = f(x), you should be able to describe the graph of y = f(x + 5) + 4.
- Also, basic geometry is a must (Circles, triangles, parallelograms, angle finding, areas and volumes).
- The number two thing you need is to become really good in Algebra II (Intermediate Algebra).
- The number three thing you need in a regular calculus class is to be comfortable with trigonometry.
(f(x+h)-f(x))/h and simplify it completely for, for starters, functions like
Sqrt[x], 1/x, x^2, x^3, 1/x^2, and -x^2-3x+1.
You should understand the difference between
x+1
and
(x^2-1)/(x-1).
You should be able to graph basic functions like
x^n (n integer), x^n (n rational), a x^2+b x+c, Trig[x] (Trig=one of the six circular functions from trigonometry), Exp[x], Log[x], and for an f listed above, something of the form a f[b x+c] + d.
You should be able to solve algebraic inequalities like
(x^2+4x+4)/(x-1) > 0.
http://www.intmath.com/Calculus/Calculus-intro.php
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