MATH-M 311 Lecture Notes - Lecture 15: Trigonometric Functions, Directional Derivative, Solution Set
Document Summary
Section 14. 6 notes- directional derivatives and the gradient vector. Directional derivative- slope of at point in direction: where is moving along line in direction by multiples of, common to write where instead of for ; analogous for variables. We want to understand the rate of change in the non-axis direction at the specified point . Ex: if is a point close to , then, let and. Rate of change of at in direction o. What is the slope of at the point in the direction ? o: secant line has slope, distance from to point. Distance between 2 vectors = magnitude of difference o: let where no absolute value needed if. Notice is what we want to calculate to get -direction slope at. Gradient- for , vector-valued function formed by that maps: takes and gives back a vector in same dimension, notated as ( nabla , ex. Formula for calculating directional derivatives: observation- if and and are fixed, then o.
