
Recent Posts
Archives
 March 2023
 January 2023
 May 2020
 April 2020
 March 2020
 June 2018
 July 2016
 June 2016
 May 2016
 March 2015
 February 2015
 January 2015
 December 2014
 December 2013
 November 2013
 July 2013
 June 2013
 May 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
Categories
Meta
Pages
Tag Archives: calculus
Thinking Infinitesimally – Multivariate Calculus (II)
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
Thinking Infinitesimally – Multivariate Calculus (I)
[ Background required: some understanding of singlevariable calculus, including differentiation and integration. ] The object of this series of articles is to provide a rather different pointofview to multivariate calculus, compared to the conventional approach in calculus texts. The typical … Continue reading
Posted in Notes
Tagged calculus, differentiation, intermediate, multivariate, partial differentiation
Leave a comment
What is Curvature? (II)
[ Background required: rudimentary vector calculus. ] The aforementioned definition of curvature is practical but a little aesthetically displeasing. Specifically, one seeks a definition which is independent of the parametrization of the curve. The advantage of such a definition is … Continue reading
What is Curvature? (I)
[ Background required: calculus, specifically differentiation. ] In this post, we will give a little background intuition on the definition of curvature. One possible approach is given in wikipedia, ours is another. Note that this is not IMOrelated (my apologies … Continue reading
Estimating Sums Via Integration
Background required : calculus, specifically integration By representing a sum as an area, it is often possible to estimate its size by approximating it with the area underneath a curve. For example, suppose we wish to compute the sum . … Continue reading
Number Theory and Calculus/Analysis
Background required: modular arithmetic, calculus. Once in a while, I’ll post something which offers a glimpse into more advanced mathematics. Here’s one. Example 1 For starters, we know from basic algebra that . Let’s see if there’s a corresponding result … Continue reading