Chapter 10.7, Problem 7E

Interpretation Introduction

Interpretation:

To develop the renormalization theory for functions with a fourth-degree maximum, $\text{f}\left(\text{x, r}\right){\text{ = r - x}}^{\text{4}}$. To find the approximate value of $\text{α}$ predicted by using the methods of Exercise $\text{10}\text{.7}\text{.1}$ and $\text{10}\text{.7}\text{.5}$. To estimate the first few terms in the power series for the universal function $\text{g}\left(\text{x}\right)$. To estimate the new value of $\text{δ}$ for the quartic case by numerical experimentation.

Concept Introduction:

• The power series expansion for the Quartic maxima is given by

$\text{f}\left(\text{x}\right){\text{ = 1 + c}}_{\text{1}}{\text{x}}^{\text{4}}{\text{ + c}}_2{\text{x}}^8+\mathrm{.......}$