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Monthly Archives: June 2012
“High School Mathematics”: Naive Foundations
1. It dawned on me I should specify what exactly I mean by “high school mathematics” mentioned in the “About” page. Briefly: it’s all the mathematics we learned in secondary school (well, American secondary school) plus some naive set theory. … Continue reading
Continuity for Functions of Several Variables, Partial Derivatives
1. We considered differentiating and integrating functions of a singlevariable. How? We began with the notion of a limit, and then considered the derivative. If we have a, e.g., polynomial (1) we see (2) Again we stop and reflect: this … Continue reading
Posted in Calculus, Partial Derivative, Vector Calculus
Tagged Continuity, Partial Derivative
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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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