Vector-Valued Functions
Functions from Rⁿ to Rᵐ and Their Derivatives
Extending differentiation to functions with vector outputs. This chapter covers the Jacobian for vector-valued functions, local linear approximation in the vector setting, trajectories, and the geometry of vector-valued maps.
Sections
Vector-Valued Functions
10 min · 2 quiz questions
The Jacobian for Vector-Valued Functions
12 min · 2 quiz questions · Interactive diagram
Local Linear Approximation for Vector-Valued Functions
10 min · 2 quiz questions
U-Derivative for Vector-Valued Functions
8 min · 2 quiz questions
The 2×2 Case
10 min · 2 quiz questions · Interactive diagram
Trajectories
8 min · 2 quiz questions · Interactive diagram
The Tangent Vector
10 min · 2 quiz questions
Geometry of Trajectories
10 min · 2 quiz questions · Interactive diagram
Alternative Derivation of the Tangent Vector
8 min · 2 quiz questions