Tag Archives: multivariate

Basic Analysis: Limits and Continuity (3)

Posted on November 25, 2012 by limsup

Let’s consider multivariate functions where . To that end, we need the Euclidean distance function on Rn. If x = (x1, x2, …, xn) is in Rn, we define: Note that |x| = 0 if and only if x is the zero vector 0. Now we are ready … Continue reading →

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Thinking Infinitesimally – Multivariate Calculus (II)

Posted on April 17, 2012 by limsup

Chain Rule for Multivariate Calculus We continue our discussion of multivariate calculus. The first item here is the analogue of Chain Rule for the multivariate case. Suppose we have parameters f, u, v, x, y, z. Suppose {u, v} are independent parameters (in particular, … Continue reading →

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Thinking Infinitesimally – Multivariate Calculus (I)

Posted on April 15, 2012 by limsup

[ Background required: some understanding of single-variable calculus, including differentiation and integration. ] The object of this series of articles is to provide a rather different point-of-view to multivariate calculus, compared to the conventional approach in calculus texts. The typical … Continue reading →

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