linear approximation
(1.5 hours to learn)
Summary
A function is differentiable at a point x if it can be approximated by a linear function around x. The linear approximation can be computed in terms of the partial derivatives at x.
Context
This concept has the prerequisites:
- partial derivatives (The linear approximation is computed from partial derivatives.)
- dot product (The linear approximation is given in terms of a dot product.)
- limits and continuity in R^n (Differentiability requires continuous partial derivatives.)
Core resources (read/watch one of the following)
-Paid-
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location:
Section 13.6, "Increments and linear approximation," pages 889-895
→ Multivariable Mathematics
A textbook on linear algebra and multivariable calculus with proofs.
Location:
Section 3.2, "Differentiability," pages 87-95
Supplemental resources (the following are optional, but you may find them useful)
-Free-
→ MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
Location:
Lecture 27, "Approximation formula"
See also
-No Additional Notes-