This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 251 Section 4: Review for Test4 Test4 covers Section11.4 through Section12.2 (except for Section11.8). Here is the highlight of each section. Section11.4 Find the equation of the tangent plane to a given surface (the formula will be given in the test); nd the dierential of a function. Section11.5 Find the partial derivatives by the Chain Rule; write out the Chain Rule for a given composite function. Section11.6 Find the directional derivative; nd the gradient of a given function and be aware of that f gives the direction along which the maximum rate of change occurs; nd the maximum rate of change i.e.  f . Section11.7 Find the local maximum and minimum values and saddle points of a function (The Second Derivative Test will be given.); nd extreme values for practical problems (Example 4, 5). Section12.1 Evaluate iterated integrals; evaluate double integrals over rectangle by iterated integrals. Section12.2 Evaluate double integrals over general regions (type I and type II). Here is a list formulas and facts that you need to memorize. (a) The dierential of z = f (x, y ) is dz = fx (x, y )dx + fy (x, y )dy . (b) The gradient of f (x, y ) is
f = fx , fy . (c) The directional derivative of f in the direction of a unit vector u = a, b is
Du f = f · u = fx a + fy b.
1 (d) A point (a,b) is called a critical point of f (x, y ) if fx (a, b) = 0 and fy (a, b) = 0. Finding critical points of some function is usually the rst step to nd the extreme values. (e) Fubini's Theorem If f is continuous on the rectangle R = {(x, y )a ≤ x ≤ b, c ≤ y ≤ d}, then
¨ ˆ
d ˆ b ˆ bˆ
a d f (x, y )dA =
R c a f (x, y )dxdy =
c f (x, y )dydx. (f) If f is continous on a type I region D = {(x, y )a ≤ x ≤ b, g1 (x) ≤ y ≤ g2 (x)} then
¨ ˆ bˆ
a g2 (x) f (x, y )dA =
D g1 (x) f (x, y )dydx. If f is continous on a type II region D = {(x, y )c ≤ y ≤ d, h1 (y ) ≤ x ≤ h2 (y )} then
¨ ˆ
d ˆ h2 (y ) f (x, y )dA =
D c h1 (y ) f (x, y )dxdy. 2 ...
View
Full
Document
This note was uploaded on 05/14/2010 for the course MATH 251 taught by Professor Cghen during the Spring '09 term at WVU.
 Spring '09
 CGHEN
 Math

Click to edit the document details