Taylor Series

How does a calculator find $\sin(0.3)$? Learn to approximate curves with lines, then parabolas, then polynomials of any degree. Build the famous series for $e^x$, $\sin x$ and $\cos x$, choose the best centre, see where approximations break down, measure their errors, and use them to uncover $E = mc^2 + \tfrac12 mv^2$ and Euler's formula.