(Recall the example from mechanics of work: W 1* ff I?" - allj.
rm. 2.0% + Age. is) - <de + an)
In order to evaluate this, we need to know Am and AL, as a function of position and to dene
the path of integratio
You should know how the trigonometric functions are dened with respect to a right triangle.
sinB :3 = cosa
coed = i:- = sina
tan6 = g = cote:
c2 0052 6 + c2 sin2 6 = c2 or
cos2 6? + sin2 6 = -1
You should be familiar with a 3,4,5 tri
Example: 102 = 100. This gives A = 10, (the base), a: = 2, (the power) and y = 100, (the
Note: Knowledge of the BASE is crucial.
In mathematics, there is another common base, given by the symbol 6, where e i 2.71828.
1093(3) = 1.0986 means th
In other words, 101'092 = 1/101'092 = 0.081. Does this make sense? We know that
logm(0.l) = l and log10(0.01) = 2. We then expect the answer to lie between 1 and *2.
CHANGE OF BASE
Suppose we have a number, y. We can express y in terms of base 10 or base
I Polar Coordinates
The coordinate of a point on a plane can be expressed in Cartesian coordinates as (rmry)
where TI is the distance of the point from the y axis, and 7", is the distance of the point
from the 9: axis. We can also express the vector from
H Vectors (Two Dimensions)
There are several alternative equivalent ways to write vectors:
1'7 = (Vmavir)
17 = (V 0056, Vsintl)
i7 = IQE+Vy
where V =[ l7 |= length or magnitude of 17 This is a positive number.
i and 3 are unit vectors dened to point in
L Surface Integrals
You are not expected to know this material at the start of the course. The needed material
will be covered in the course. You will be responsible for this after the material has been
Let us begin by examining a plane as shown o
J Vector Functions
The function Elf) 2 (134?), Ey(i"),Ez(F) is a vector function (or vector eld) with three
components. Each component is itself a function of the coordinate i7 = (m, y, 2). Thus EU")
is actually three functions.
0 E3307) for the micompone
You should always be able to draw the sine or cosine curves for one cycle, (0 > 360),
Sit/2 3n 71r/2
Figure 1: (a) Sine Curve. (b) Cosine Curve.
D Binomial Expansion
n nlb _1 n2b2
0! 1! 2! +"'
The binomial e