Calculus Articles

Tag Archive for: calculus

Epsilontic limits and continuity

Epsilontic – Limits and Continuity

/
1 Comment
Abstract I remember that I had some difficulties moving from school mathematics to university mathematics. From what I read on PF through the years, I…
calc precalc

Beginners Guide to Precalculus, Calculus and Infinitesimals

/
3 Comments
Introduction I am convinced students learn Calculus far too late.   In my view, there has never been a good reason for this.In the US, they go through…
Infinitesimals

What Are Infinitesimals – Simple Version

/
5 Comments
Introduction When I learned calculus, the intuitive idea of infinitesimal was used. These are real numbers so small that, for all practical purposes (say…
history of numbers

Counting to p-adic Calculus: All Number Systems That We Have

/
0 Comments
An entire book could easily be written about the history of numbers from ancient Babylon and India, over Abu Dscha'far Muhammad ibn Musa al-Chwarizmi (##\sim…
hypercube integral

A Novel Technique of Calculating Unit Hypercube Integrals

/
1 Comment
Introduction In this insight article, we will build all the machinery necessary to evaluate unit hypercube integrals by a novel technique. We will first…
Riemann Hypothesis

The Extended Riemann Hypothesis and Ramanujan’s Sum

/
2 Comments
Riemann Hypothesis and Ramanujan's Sum ExplanationRH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line. ERH: All…
valentines reflections graphs

Valentine’s Reflections: Mathematical Matters of the Heart

/
4 Comments
Introduction Being a somewhat geeky Maths 'nerd', I spent days leading up to Valentine's Day trying to find a Maths function appropriate to the day. In…
integration by parts

What is Integration By Parts? A 5 Minute Introduction

/
0 Comments
Definition/Summary In this article, we shall learn a method for integrating the product of two functions. This method is derived from the 'product rule'…
surface integral

Demystifying Parameterization and Surface Integrals

/
3 Comments
Introduction This article will attempt to take the mystery out of setting up surface integrals. It will explain the basic ideas underlying surface integration…

Demystifying the Chain Rule in Calculus

/
7 Comments
Introduction There are a  number of posts on PF involving a general confusion over the multi-variable chain rule.  The problem is often caused by…
physicsturnedmath

Trials and Tribulations of a Physicist who Became a Math Geek

/
6 Comments
How did I go from the brink of changing my major from physics to ceramics (no more math) to the Math faculty of the Air Force Academy? How did I go from…
differentiable function 2

A Continuous, Nowhere Differentiable Function: Part 2

/
2 Comments
This is Part 2 of a series of articles in which the goal is to exhibit a continuous function that is nowhere differentiable and to explore some interesting…
differentiable function

A Continuous, Nowhere Differentiable Function: Part 1

/
12 Comments
When studying calculus, we learn that every differentiable function is continuous, but a continuous function need not be differentiable at every point.…