Multivariable Calculus Note

Vectors and the Geometry of Space

Vector

Inner product

Norm

Cross Product

Line

Plane

Vector-Valued Functions and Motion in Space

Parametric Curve

Derivative of Vector Function

Antiderivative of Vector Function

Arc Length

Curvature of Curves

Unit Tangent Vector

Principal Unit Normal Vector

Binormal Vector

Torsion of Curves

TNB Frame

Tangential and Normal Components of Acceleration

Frenet-Serret Formulas

Partial Derivatives

Interior

Boundary

Level Set

Limit of a Function

Continuous Function

Differentiability

Directional Derivative

Partial Derivative

Symmetry of Second Derivatives

Increment Theorem

Chain Rule

Implicit Function Theorem

Gradient

Tangent

Approximation

Extremum

Critical Point

Saddle Point

First-Derivative Test

Second-Derivative Test

Method of Lagrange Multipliers

Taylor Series for Two Variables

Multiple Integrals

Fubini’s Theorem