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Partial Differentiation (Metric)

Learn, or revise, the principles and techniques of partial differentiation.

Principles

The partial derivatve, the chain rule and higher derivatives.

The partial derivatives \(\partial z/\partial x\) and \(\partial z/\partial y\).

The Chain Rule for partial derivatives; change of variable.

The higher derivatives \(\partial^2z/\partial x^2\), \(\partial^2z/\partial x\partial y\), etc.

Techniques

Finding and classifying stationary points on surfaces.

Finding stationary points on surfaces by solving \(\partial z/\partial x = \partial z/\partial y = 0\).

Classifying stationary points by considering \(z_{xx}\,z_{yy}-{z_{xy}}^2\).