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Three Dimensional Spaces
In this section we will start taking a much more detailed look at 3-D space or R3). This is a major topic for mathematics as a good portion of Calculus III is completed in three (or higher) dimensional space.
We will be looking at the equations of graphs in 3-D (3 dimensional) space also vector valued functions and how we do calculus along with them. We will as well be taking a look at a couple of new coordinate systems for 3-D space.
This is the only section that exists in two places in my notes.
Here is a listing of topics in this section.
a. The 3-D Coordinate System
b. Equations of Lines
c. Equations of Planes
d. Quadric Surfaces
e. Functions of Several Variables
f. Vector Functions
g. Calculus with Vector Functions
h. Tangent, Normal and Binormal Vectors
i .Arc Length with Vector Functions
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s
log base 5 (3-2x) + log base 5 (2+x) = 1
Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other at P, externally or internally. Construction: join OP and O 1 P . Proof : we know that if two circles touch each
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The area of a parallelogram can be expressed as the binomial 2x 2 - 10x. Which of the following could be the length of the base and the height of the parallelogram? To ?nd out
Write down the system of differential equations for the population of both predators and prey by using the assumptions above. Solution We will start off through letting that
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