Calculus Articles

Tag Archive for: calculus

Epsilontic limits and continuity

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…
calc precalc

Beginners Guide to Precalculus, Calculus and Infinitesimals

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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

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

The Art of Integration

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Abstract My school teacher used to say "Everybody can differentiate, but it takes an artist to integrate." The mathematical reason behind this phrase…
history of numbers

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

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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

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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

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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

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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

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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

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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

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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…
integraltrick

Trick to Solving Integrals Involving Tangent and Secant

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This little trick is used for some integration problems involving trigonometric functions is probably well-known, but I only learned it yesterday. So…
physicsturnedmath

Trials and Tribulations of a Physicist who Became a Math Geek

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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…
studymath2

How to Self-Study Calculus: Topics and Book Guide

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To self-study calculus, work through four core areas in order: differentiation, integration, sequences and series, then multivariable calculus. Each builds…
differentiable function 2

Nowhere Differentiable Functions: Fejér Kernel & Cesàro Sums

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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

Constructing a Continuous but Nowhere Differentiable Function

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