Advanced Engineering Mathematics, 7th Edition

11.3 Linearization and Local Stability

INTRODUCTION

The key idea in this section is that of linearization. Recall from calculus and Section 2.6, a linearization of a differentiable function f(x) at a number x₁ is the equation of the tangent line to the graph of f at the point:

For x close to x₁ the points on the graph of f are close to the points on the tangent line so values y(x) obtained from the equation of the tangent line are said to be local linear approximations to the corresponding function values f(x). Similarly, a linearization of a function of two variables f(x, y) that is differentiable at a point (x₁, y₁) is the equation of the ...