Science and Math Tutorials

Here contain the expert tutorials for all science and math disciplines. Tutorials are technical and focus on one narrow skill. It’s more like a how-to than a guide.

Data Structures Programming

Intro to Data Structures for Programming

IntroductionIn the first part of this series, I talked about…
rotational mechanics

An Example of Servo-Constraints in Mechanics

Servo-constraint was invented by Henri Beghin in his PhD thesis…
unity orbital mechanics

Orbital Mechanics in Unity Game Engine for Augmented Reality

In this post I’ll go over implementing basic orbital mechanics…
walter lewin

A New Interpretation of Dr. Walter Lewin's Paradox

Much has lately been said regarding this paradox which first…

Calculating the Spin of Black Hole Sagittarius A*

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

Solving Einstein's Field Equations in Maxima

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

Rindler Motion in Special Relativity: Rindler Coordinates

Our destination In our last article, Hyperbolic Trajectories,…

Rindler Motion in Special Relativity: Hyperbolic Trajectories

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

Statistical Mechanics: Equilibrium Systems

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

Demystifying the Chain Rule in Calculus

Introduction There are a  number of posts on PF involving…

Make Units Work for You

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

The Homopolar Generator: An Analytical Example

Introduction It is surprising that the homopolar generator,…

A Journey to The Manifold SU(2): Representations

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

Further Sums Found Through Fourier Series

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

An Integral Result from Parseval's Theorem

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

The Joy of Processing

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

Relativity Using the Bondi K-calculus

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

The Pantheon of Derivatives - Part V

  Important Theorems - biased, of course Implicit…

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

Traditional presentations of special relativity place emphasis…

The Pantheon of Derivatives - Part IV

  Lie Derivatives A Lie derivative is in general the…

The Pantheon of Derivatives - Part III

  Some Topology Whereas the terminology of vector…

The Pantheon of Derivatives - Part II

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

The Pantheon of Derivatives - 5 Part Series

  Differentiation in a Nutshell I want to gather the…

Trick to Solving Integrals Involving Tangent and Secant

This little trick is used for some integration problems involving…

Frames of Reference: Linear Acceleration View

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

Fabry-Perot and Michelson Interferometry: A Fundamental Approach

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

Using the Fourier Series To Find Some Interesting Sums

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

The Schwarzschild Geometry: Physically Reasonable?

 In the last article, we looked at various counterintuitive…

The Schwarzschild Geometry: Coordinates

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

The Schwarzschild Geometry: Key Properties

 Not long after Einstein published his Field Equation,…

Partial Differentiation Without Tears

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

Solving the Cubic Equation for Dummies

Everybody learns the "quadratic formula" for solving equations…

Explaining How Rolling Motion Works

Although rolling wheels are everywhere, when most people are…

Grandpa Chet's Entropy Recipe

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

Orbital Precession in the Schwarzschild and Kerr Metrics

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

Precession in Special and General Relativity

The Absolute DerivativeIn relativity we typically deal with…

Tetrad Fields and Spacetime

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

Omissions in Mathematics Education: Gauge Integration

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

Relativity on Rotated Graph Paper

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

Explaining the General Brachistochrone Problem

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

Some Misconceptions on Indefinite Integrals

Integration is an incredibly useful technique taught in all calculus…

Basic Kinematics in Classical Mechanics

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