MAT- '3'; E U
T. Zakon' 2.
cfw_-0 curl/5 C!
5 who: 2: 40:1)
Curve. C: "
Ee (X)= neCXJlo)
in 3,133 Plane. Hana Yzy
1 3 VJ:
X - j
. . . . . 5f .
Denition and geometric interpretation of the partial derivative 6; at the pomt (ono)
Let (xa ,
GRADIENT VECTOR AND DIRECTIONAL DERIVATIVE
Let z = f ( x, y ) be a differentiable function, and let
P0 ( x0 , y 0 ) be a point in the domain of f .
( x0 , y 0 ) in the direction of a unit vector
f ( x0 + hu1 , y 0 + hu 2 ) f ( x0 , y 0 )
GEOMETRIC APPLICATIONS OF GRADIENTS
TANGENT LINES, TANGENT PLANES, NORMAL LINES
There are several ways of finding an equation of tangent and normal line to a curve in the plane. Some of
these were taught in Calculus I, but not all of them
LEAST SQUARES APPOXIMATION
A common problem in experimental work is to obtain a functional relationship y = f (x ) between two variables
x and y , by finding a curve of best fit to a given set of observations.
Line of Best Fit (Regressio
MATLCU iNCREMENTS AND DIFFERENTIALS
Function 3/ = f(x) of one variable cfw_Recall from Calculus I a
When the independent variable changes from 3:0 to x0 + Ax
the dependent variable changes by A? = f0:a + Ax) fora) .
If y = x) = f(x0)+ f'(xo )(x
REPERTOIRE OF FAMILIAR TAYLOR (MACLAURIN) SERIES
= 1+ x + x2 + x3 +L
xn = 1 x + x2 x3 +L
Arc tan x =
( 1) n x 2 n +1
x3 x5 x7
L , x [ 1, 1]
2n + 1
ln(1 + x ) =
( 1) n +1
STATEMENTS AND PROOFS OF TESTS OF CONVERGENCE AND
DIVERGENCE FOR INFINITE SERIES OF NUMBERS 1
The n-th term test for divergence (applies to all series)
lim a n 0 then the series
an automatically diverges.
This test can be ap
BASIC IDEA: Suppose a function of one or more variables satisfies an equation relating the dependent and
independent variables, and suppose it is difficult or impossible to express the dependent variable
MAT 201-LCU MS
STUDY GUIDE FOR TEST I
NOTE: The best way to prepare for the test is to read your notes, and concentrate on the examples in
them (they are central to the topic). You might try to re-do these examples, and check against
STUDY GUIDE FOR TEST II
NOTE: Textbook reference: Sections 12.6, 13.1 13.4 (not including Keplers Laws), and sections 14.1
14.6. Concentrate on items in the textbook that are also listed in the study guide. Also consult