Math100, 3-Dimensional Space; Vectors
1.1
Rectangular Coordinates
Points in the space are presented by their coordinates, similar to the case for
points in a plane. Take three lines in the space which are mutually perpendicular
and we call them the x-axis
Math100, Vector-Valued Functions
2.1
Curves
Denition 2.1 A parametric representation of a curve (or a curve) is a function r, in which a number is plugged in and a vector is returned (or a vectorvalued function).
Remark 2.2 Let r be a vector-valued functi
Math100, Partial Derivatives
3.1
Functions of Two or More Variables
Denition 3.1 f is a function in n variables if f is a function in which a
vector in the n-dimensional space is plugged in and a number is returned.
Denition 3.2 Let f be a function in n v
Math100, Multiple Integrals
4.1
Double Integrals
Denition 4.1 Let f be a function in two variables, R be a region in the plane.
The integral of f over R, denoted by R f or R f (x, y)dxdy, is dened to be the
limit of
i
f (a point in the ith rectangle) (are
Math100, Vector Calculus
5.1
Vector Fields
Denition 5.1 A vector eld in the n dimensional space is a function in which
a vector in the n dimensional space is plugged in and a vector in the n dimensional space is returned.
Example 5.2 Let be a function in
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Final Exam of Math100 (All Lecture Sections, Fall 2008)
Lecture section:
Full Name:
Student ID:
1. Evaluate the double integral
2
4 x2
0
4 x2
x 2 dydx by converting to polar coordinates.
(10 points)
Solution: Th
Market Equilibrium
Supply & Demand
y also written as f (x)
Quadratic (Curve with 1 TP)
Linear (Straight Line)
Demand curve
m>0
Put y = 0 to find x value
Put x = 0 to find y value
b 2 - 4ac < 0
Does not cut/intersect
Discriminant (b 2 - 4ac)
b 2 - 4ac = 0