This preview shows pages 1–3. Sign up to view the full content.
1
The Gradient and Applications
±
This unit is based on Sections 9.5 and 9.6 , Chapter 9.
±
All assigned readings and exercises are from the textbook
±
Objectives
:
Make certain that you can define, and use in context, the terms,
concepts and formulas listed below:
1.
find the gradient vector at a given point of a function.
2.
understand the physical interpretation of the gradient.
3.
find a multivariable function, given its gradient
4.
find a unit vector in the direction in which the rate of change
is greatest and least, given a function and a point on the
function.
5.
the rate of change of a function in the direction of a vector.
6.
find normal vector and tangent vectors to a curve
7.
write equations for the tangent line and the normal line.
8.
find an equation for the tangent plane to a surface
±
Reading
:
Read Section 9.5, pages 474482.
±
Exercises
:
Complete problems 9.5 and 9.6
±
Prerequisites
: Before starting this Section you should
. . .
9
familiar with the concept of partial differentiation
9
be familiar with vector functions
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Directional Derivatives: definition
±
We are interested in how
T
changes from one point to another.
T
=20
T
=25
T
=15
A
B
±
Consider the temperature
T
at
various points of a heated metal
plate.
±
Some contours for
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '10
 S.SamuelLi

Click to edit the document details