Multivariable Calculus Tags

# Multivariable Calculus Tags

## Vector geometry

- Vectors and vector arithmetic
- Dot product, length, and unit vectors
- Cross product
- Coordinate systems

## Calculus of vector valued functions

- Parameterized curves
- Limits and continuity
- Derivatives
- Integrals
- Arc length and curvature
- Frames, motions, and other applications

## Concepts for multivariable functions

- Notation, domain, and range
- Surfaces
- Quadratic surfaces
- Surfaces in other coordinate systems
- Parameterized surfaces
- Traces, contours, and level sets

## Differentiation of multivariable functions

- Limits and continuity
- Partial derivatives
- Chain rule
- Differentiability, linearization and tangent planes
- Directional derivatives and the gradient
- Extreme values and optimization
- Lagrange multipliers and constrained optimization

## Integration of multivariable functions

- Double integrals over rectangles
- Iterated integrals and Fubini's theorem
- Double integrals over general regions
- Double integrals in polar
- Triple integrals
- Change of variable
- Triple integrals in cylindrical and spherical
- Applications of double integrals
- Applications of triple integrals

## Vector fields

- Graphs, flows lines, and level surfaces
- Identifying extrema from graphs

## Vector calculus

- Derivatives
- Line integrals
- Conservative vector fields
- Applications of line integrals
- Curl and divergence
- Surface integrals of scalar fields
- Surface integrals of vector fields

## Fundamental theorems

- Line integrals
- Green's theorem
- Stokes' theorem
- Divergence theorem