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