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Category Archives: Geometry
Curves, Velocity, “Classical Kinematics”
1. Curves. We are interested in describing the motion of my car. Well, everyone is interested in the motion of my car. How can we describe it mathematically? First we approximate the car as a point. The pointlike car moves … Continue reading
Posted in Calculus, Curves, Geometry, Vector Calculus
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Surfaces (…well, “Quadrics”)
1. Let where , , …, are all independent variables. Then the “Domain” of is the set of tuples . Note that an ordered pair is (1) The set of corresponding values is the “Range” (or Codomain) of the function. … Continue reading
Posted in Calculus, Geometry, Vector Calculus
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Constructing Planes
1. We can use vectors and the cross product to construct planes quite easily.
Line Constructions
1. We will use our knowledge of vectors to construct lines in 3space, i.e., threedimensional Euclidean space.
Constructing Orthogonal Vectors, Geometric Implications
1. Last time we ended with discussing how to project a vector onto another. So if we consider projecting onto , we can write this as (1) Observe, we have another vector constructed (2) which is orthogonal to . We … Continue reading
Introducing Vectors for Geometry
We will discuss vectors, which for our purposes right now are thought of as a directed line segment. Its length corresponds to its magnitude, and it encodes information regarding orientation. So we can represent, e.g., “The wind blowing 30 miles … Continue reading
Posted in Geometry, Vector Calculus
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