Calculus 3

Partial derivatives

Functions of several variables

\( \textnormal{A function } f \textnormal{ of two variables is a rule that assigns to each ordered pair of real numbers (x, y) in a set } H \textnormal{ a unique real number denoted by f(x, y). The set } H \textnormal{ is the domain of f and its range is the set of values which } f \textnormal{ takes, that is, } \{ \, f(x, y) \, | \, (x, y) \, \epsilon \, H \, \} \qquad (\textnormal{Definition of multivariable function}) \)

Lmits and continuity

Partial derivatives

Tangent planes and linear approximations

Chain rule

Directional derivatives and the gradient vector

Maximum and minimum values

Lagrange multipliers