4.2 Taylor series and complex numbers chapter contents

At the end of this chapter you will have:

$\diamond$ calculated higher-order derivatives;

$\diamond$ learned the Taylor series formula;

$\diamond$ calculated Maclaurin series;

$\diamond$ deduced the general binomial theorem from Maclaurin’s formula;

$\diamond$ learned the notions of local maximum and minimum;

$\diamond$ used Taylor’s theorem to classify stationary points;

$\diamond$ used calculus to sketch graphs of functions;

$\diamond$ reviewed the arithmetic of complex numbers;

$\diamond$ solved the real quadratic equation using complex numbers;

$\diamond$ used the complex exponential to express trigonometric functions;

$\diamond$ used De Moivre’s theorem to simplify trigonometric expressions;

$\diamond$ learned the principle of linear superposition for linear homogeneous differential equations;

$\diamond$ solved homogeneous second order linear differential equations via the auxiliary equation .