mathematics self-study Articles

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calculus

How to Solve Second-Order Partial Derivatives

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Introduction A frequent concern among students is how to carry out higher order partial derivatives where a change of variables and the chain rule are…
lerch and zeta functions

The Analytic Continuation of the Lerch and the Zeta Functions

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The Analytic Continuation of the Lerch Transcendent and the Riemann Zeta FunctionIntroduction In this brief Insight article the analytic continuations…
Integral Representations of Some Special Functions

A Path to Fractional Integral Representations of Some Special Functions

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0. Introduction As for the reference material I have used the text Special Functions by Askey, Andrews, and Roy which covers much of the theorems here…
Calculus Therom

A Numerical Insight for the Fundamental Theorem of Calculus

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The purpose of this article is not to provide some rigorous statement, neither a rigorous clever proof of the fundamental theorem of calculus. It is rather…
tensor calculus

The 10 Commandments of Index Expressions and Tensor Calculus

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Having more than 10 years of experience in teaching vector and tensor calculus and special and general relativity, I have noted that many people have the…
Maxwell equations

The Homopolar Generator: An Analytical Example

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Introduction It is surprising that the homopolar generator, invented in one of Faraday's ingenious experiments in 1831, still seems to create confusion…
whatisatensor

What Is a Tensor?

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Let me start with a counter-question. What is a number? Before you laugh, there is more to this question as one might think. A number can be something…
cubicfunction

Solving the Cubic Equation for Dummies

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Everybody learns the "quadratic formula" for solving equations of the form [itex]A x^2 + B x + C = 0[/itex], even though you don't really need such a formula,…
omissionguage

Omissions in Mathematics Education: Gauge Integration

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The current (pure) mathematics curriculum at the university is well established. Most of the choices made are sensible. But still, there are some important…
integralmisconceptions

Some Misconceptions on Indefinite Integrals

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Integration is an incredibly useful technique taught in all calculus classes. Nevertheless, there are certain paradoxes involved with integration that…
groupsandgeometry

Exploring the Relationship Between Group Theory and Geometry

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There is a very deep link between group theory and geometry. Sadly, this link is not emphasized a lot in most courses of group theory, even though it is…
selfstudy

5 Problems with Self Studying Mathetmatics

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For several years already I have been trying to help people who have been self-studying math. I did this completely freely with no compensation for me.…
highschoolmath

In High School and Want to Do Advanced Mathematics?

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This insight is written for high school students who don't feel very challenged by their high school courses. Or maybe those high school students who want…
studymath

How to Self-Study Basic High School Mathematics

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  IntroductionWe often get questions here from people self-studying mathematics. One of those questions is what of mathematics should I study…
studymath2

A Guide to Self Study Calculus

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  We often get questions here from people self-studying mathematics. One of those questions is what of mathematics should I study and in what…
studymath1

The Essential Guide to Self Study Mathematics

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  How to self-study mathematics? People self-study mathematics for a lot of reasons. Either out of pure interest, because they want to get ahead,…