\( \newcommand{\sech}{\operatorname{sech}} \) \( \newcommand{\inverse}[1]{#1^\leftarrow} \) \( \newcommand{\<}{\langle} \) \( \newcommand{\>}{\rangle} \) \( \newcommand{\vect}{\mathbf} \) \( \newcommand{\veci}{\mathbf{\hat ı}} \) \( \newcommand{\vecj}{\mathbf{\hat ȷ}} \) \( \newcommand{\veck}{\mathbf{\hat k}} \) \( \newcommand{\curl}{\operatorname{curl}\,} \) \( \newcommand{\dv}{\operatorname{div}\,} \) \( \newcommand{\detThree}[9]{ \operatorname{det}\left( \begin{array}{c c c} #1 & #2 & #3 \\ #4 & #5 & #6 \\ #7 & #8 & #9 \end{array} \right) } \) \( \newcommand{\detTwo}[4]{ \operatorname{det}\left( \begin{array}{c c} #1 & #2 \\ #3 & #4 \end{array} \right) } \)

MA 227 Standard S06

Linearization
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At the end of the course, each student should be able to…

  • S06: Lineariz. Compute the linearization of a two-variable real-valued function at a point and use it for approximation.

S06: Linearization

  • Differentiable functions \(f(x,y)\) may be approximated near a point \(P_0\) by the linearization \(L(x,y)\) defined by the tangent plane at that point.
    • Its equation is \(L(x,y)=f(P_0)+f_x(P_0)(x-x_0)+f_y(P_0)(y-y_0)\).
    • Thus if \(<x,y>\approx P_0\), then \(L(x,y)\approx f(x,y)\).

Textbook References

  • University Calculus: Early Transcendentals (3rd Ed)
    • 13.6 (exercises 25-30)