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.

rotational mechanics

An Example of Servo-Constraints in Mechanics

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

Orbital Mechanics in Unity Game Engine for Augmented Reality

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

A New Interpretation of Dr. Walter Lewin's Paradox

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Much has lately been said regarding this paradox which first…
Sagittarius_A

Calculating the Spin of Black Hole Sagittarius A*

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

Solving Einstein's Field Equations in Maxima

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A few months ago, pervect pointed me to a post by Chris Hillman…
ridler_motion2

Rindler Motion in Special Relativity: Rindler Coordinates

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Our destination In our last article, Hyperbolic Trajectories,…
ridler_motion

Rindler Motion in Special Relativity: Hyperbolic Trajectories

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Introduction: Why Rindler Motion? When students learn relativity,…
statmech1

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…
unitsworkforyou

Make Units Work for You

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

The Homopolar Generator: An Analytical Example

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Introduction It is surprising that the homopolar generator,…
manifold2

A Journey to The Manifold SU(2): Representations

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Part 1  Representations Image source: [24]  6.…
fourierseries2

Further Sums Found Through Fourier Series

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

An Integral Result from Parseval's Theorem

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

The Joy of Digital Processing

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

Relativity Using the Bondi K-calculus

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Although Special Relativity was formulated by Einstein (1905),…
deriitive5

The Pantheon of Derivatives - Part V

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  Important Theorems - biased, of course Implicit…
RelativityVariables

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

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Traditional presentations of special relativity place emphasis…
deriitive4

The Pantheon of Derivatives - Part IV

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  Lie Derivatives A Lie derivative is in general the…
deriitive3

The Pantheon of Derivatives - Part III

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  Some Topology Whereas the terminology of vector…
deriitive2

The Pantheon of Derivatives - Part II

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

The Pantheon of Derivatives - 5 Part Series

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  Differentiation in a Nutshell I want to gather the…
integraltrick

Trick to Solving Integrals Involving Tangent and Secant

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This little trick is used for some integration problems involving…
linearacceleration

Frames of Reference: Linear Acceleration View

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

Fabry-Perot and Michelson Interferometry: A Fundamental Approach

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

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)…
SchwarzschildGeometry4

The Schwarzschild Geometry: Physically Reasonable?

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 In the last article, we looked at various counterintuitive…
SchwarzschildGeometry2

The Schwarzschild Geometry: Coordinates

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 At the end of part 1, we looked at the form the…
SchwarzschildGeometry1

The Schwarzschild Geometry: Key Properties

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 Not long after Einstein published his Field Equation,…
partial-differentiation

Partial Differentiation Without Tears

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

Solving the Cubic Equation for Dummies

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Everybody learns the "quadratic formula" for solving equations…
rollingmotion

Explaining How Rolling Motion Works

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Although rolling wheels are everywhere, when most people are…
entropy

Grandpa Chet's Entropy Recipe

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

Orbital Precession in the Schwarzschild and Kerr Metrics

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

Precession in Special and General Relativity

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The Absolute DerivativeIn relativity we typically deal with…
spacetimetetrad

Tetrad Fields and Spacetime

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

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…
Brachistochrone

Explaining the General Brachistochrone Problem

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

Some Misconceptions on Indefinite Integrals

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Integration is an incredibly useful technique taught in all calculus…
basickinematics

Basic Kinematics in Classical Mechanics

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

Presenting a Rare Kinematic Formula

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Here we present some useful kinematic fact which is uncommon…