Tag Archive for: calculus
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Epsilontic – Limits and Continuity
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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…
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Beginners Guide to Precalculus, Calculus and Infinitesimals
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](https://www.physicsforums.com/insights/wp-content/uploads/2023/05/Infinitesimals.png)
What Are Infinitesimals – Simple Version
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](https://www.physicsforums.com/insights/wp-content/uploads/2022/09/history-of-numbers.png)
Counting to p-adic Calculus: All Number Systems That We Have
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…
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A Novel Technique of Calculating Unit Hypercube Integrals
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](https://www.physicsforums.com/insights/wp-content/uploads/2022/04/Riemann-Hypothesis.png)
The Extended Riemann Hypothesis and Ramanujan’s Sum
Riemann Hypothesis and Ramanujan's Sum ExplanationRH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line.
ERH: All…
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Valentine’s Reflections: Mathematical Matters of the Heart
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](https://www.physicsforums.com/insights/wp-content/uploads/2019/12/integration_by_parts.png)
What is Integration By Parts? A 5 Minute Introduction
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](https://www.physicsforums.com/insights/wp-content/uploads/2019/04/surface_integral.png)
Demystifying Parameterization and Surface Integrals
Introduction
This article will attempt to take the mystery out of setting up surface integrals. It will explain the basic ideas underlying surface integration…
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Demystifying the Chain Rule in Calculus
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…
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Trials and Tribulations of a Physicist who Became a Math Geek
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…
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A Continuous, Nowhere Differentiable Function: Part 2
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…
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A Continuous, Nowhere Differentiable Function: Part 1
When studying calculus, we learn that every differentiable function is continuous, but a continuous function need not be differentiable at every point.…