# Tutorials

### A New Interpretation of Dr. Walter Lewin's Paradox

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Much has lately been said regarding this paradox which first…

### Calculating the Spin of Black Hole Sagittarius A*

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This Insight takes a look at how it is possible to calculate…

### Solving Einstein's Field Equations in Maxima

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A few months ago, pervect pointed me to a post by Chris Hillman…

### Rindler Motion in Special Relativity: Rindler Coordinates

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Our destination In our last article, Hyperbolic Trajectories,…

### Rindler Motion in Special Relativity: Hyperbolic Trajectories

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Introduction: Why Rindler Motion? When students learn relativity,…

### Statistical Mechanics: 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): Representations

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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 Digital 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: Physically Reasonable?

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In the last article, we looked at various counterintuitive…

### The Schwarzschild Geometry: Coordinates

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

### The Schwarzschild Geometry: Key Properties

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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 How Rolling Motion Works

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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…

### Basic Kinematics in Classical Mechanics

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There is an interesting thing in teaching of Classical Mechanics.…