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Getting Started with Calculus

Calculus uses quite a few of the skills and concepts learnt from Algebra. It is recommended that you know how to transpose and factorize comfortably. Knowing about polynomial, rational, exponential and logarithmic functions is also useful.

In order to become better at Mathematics, we need to care about the language used. New students often take the terminology for granted and this cripples them in the long run. For example, the fancy phrase derivative of the product of two trigonometrical functions sounds intimidating at first but with a little extra care we can easily learn to write it into mathematical notation: $$\frac{d}{dx}(\sin{x}\cos{x})$$

$\sin{x}$ is a trig function and $\cos{x}$ is a trig function and thus multiplying them gives us the product of two trigonometrical functions. We will learn that the derivative is essentially the gradient/slope of a graph thus our fancy phrase simply means the slope of the graph of this product ($\sin{x}\cos{x}$).

It is a lack of care for the language that is the dividing line between Mathematics being a rewarding experience or an absolute nightmare. This is especially evident for Calculus.