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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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Now that we've found some of the fundamentals out of the way for systems of differential equations it's time to start thinking about how to solve a system of differential equations
1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm (Ans: 88cm) Ans: Π R 2 = 16 Π r 2 R 2 = 16 r 2
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