Master Multivariable Calculus

3-D coordinate system

3-Dimensional vectors

Dot product

Cross product

3-Dimensional lines

3-Dimensional planes

Cylindrical coordinates

Spherical coordinates

Calculus for vector functions

Tangent, normal, and binormal vectors

Arc length with vector functions

Curvature with vector functions

Tangential and normal components of acceleration

Functions of several variables

Limits and continuity of multivariable functions

Partial derivatives

Higher order partial derivatives

Differentials of multivariable functions

Chain rule for multivariable functions

Directional derivatives

Linear approximations and tangent planes

Gradient vectors

Local minima and maxima of multivariable functions

Absolute minimum and maximum of multivariable functions

Langrage multipliers

Double integrals over a rectangular region

Double integrals over a general region

Double integrals in polar coordinates

Triple integrals

Triple integrals in cylindrical coordinates

Triple integrals in spherical coordinates

Change in variables

Moment and center of mass

Surface area with double integrals