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

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Continuity for Functions of Several Variables, Partial Derivatives

1. We considered differentiating and integrating functions of a single-variable. 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 , | 1 Comment

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

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Constructing Planes

1. We can use vectors and the cross product to construct planes quite easily.

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Line Constructions

1. We will use our knowledge of vectors to construct lines in 3-space, i.e., three-dimensional Euclidean space.

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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

Posted in Calculus, Cross Product, Geometry, Vector Calculus | Tagged | 1 Comment

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 | 1 Comment