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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
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Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section
Direction Cosines This application of the dot product needs that we be in three dimensional (3D) space not like all the other applications we have looked at to this point.
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