\part{Advanced}

\chapter{Differential equations}

Similar to algebraic equations where we find a satisfying number, we can make equations involving differentiation, where we want find a satisfying function.

\chapter{Taylor series}

How are the trigonometic functions actually calculated?




\[ \frac{\pi}{4} = \sum^{\infty}_{n=1} \frac{(-1)^{n+1}}{2n-1}\]


\chapter{Advanced integration}
\section{Partial fraction decomposition}
\section{Weierstrass substitution}
\section{Recurrence relations}

Useful method to solve definite integrals that may require tedious applications of the reverse product rule.



\[\frac{\pi}{2} \prod^{\infty}_{n=1} \left(\frac{4n^2 }{4n^2 -1} \right)\]