Statistical Mechanics Part I: Equilibrium Systems

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This is the first of a multi-part series of articles intended…

Demystifying the Chain Rule in Calculus

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Introduction There are a  number of posts on PF involving…

Make Units Work for You

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How do we use units? You may see one of these speed limit signs,…

The Homopolar Generator: An Analytical Example

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Introduction It is surprising that the homopolar generator,…

A Journey to The Manifold SU(2) - Part II

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Part 1   Representations Image source: [24]   6.…

Further Sums Found Through Fourier Series

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In an earlier insight, I looked at the Fourier series for some…

An Integral Result from Parseval's Theorem

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Introduction: In this Insight article,  Parseval's theorem…

The Joy of Processing

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In the early days of the personal computer revolution, computers…

Relativity Using the Bondi K-calculus

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Although Special Relativity was formulated by Einstein (1905),…

The Pantheon of Derivatives - Part V

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Important Theorems - biased, of course Implicit…

Relativity Variables: Velocity, Doppler-Bondi k, and Rapidity

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Traditional presentations of special relativity place emphasis…

The Pantheon of Derivatives - Part IV

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Lie Derivatives A Lie derivative is in general the…

The Pantheon of Derivatives - Part III

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Some Topology Whereas the terminology of vector…

The Pantheon of Derivatives - Part II

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Generalizations Beyond ##\mathbb{R}## and ##\mathbb{C}## As…

The Pantheon of Derivatives - 5 Part Series

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Differentiation in a Nutshell I want to gather the…

Trick to Solving Integrals Involving Tangent and Secant

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This little trick is used for some integration problems involving…

Frames of Reference: Linear Acceleration View

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My previous Insight, Frames of Reference: A Skateboarder's View,…

Fabry-Perot and Michelson Interferometry: A Fundamental Approach

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Fabry-Perot Effect: The Fabry-Perot effect is usually treated…

Using the Fourier Series To Find Some Interesting Sums

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Preliminaries If f(x) is periodic with period 2p and f’(x)…

The Schwarzschild Geometry: Part 4

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In the last article, we looked at various counterintuitive…

The Schwarzschild Geometry: Part 2

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At the end of part 1, we looked at the form the…

The Schwarzschild Geometry: Part 1

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Not long after Einstein published his Field Equation,…

Partial Differentiation Without Tears

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Differentiation is usually taught quite well. Perhaps that's…

Solving the Cubic Equation for Dummies

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Everybody learns the "quadratic formula" for solving equations…

Explaining Rolling Motion

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Although rolling wheels are everywhere, when most people are…

Grandpa Chet's Entropy Recipe

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How do you determine the change in entropy for a closed system…

Orbital Precession in the Schwarzschild and Kerr Metrics

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The Schwarzschild Metric A Lagrangian that can be used to describe…

Precession in Special and General Relativity

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The Absolute Derivative In relativity we typically deal with…

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A spacetime is often described in terms of a tetrad field, that…

Omissions in Mathematics Education: Gauge Integration

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The current (pure) mathematics curriculum at the university is…

Relativity on Rotated Graph Paper

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This Insight is a follow up to my earlier tutorial Insight (Spacetime…

General Brachistochrone Problem

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Consider a problem about the curve of fastest descent in the…

Some Misconceptions on Indefinite Integrals

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Integration is an incredibly useful technique taught in all calculus…