# 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.

### Frequently Made Errors in Vectors - Elementary Use

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A vector has magnitude and direction. Pictorially,…

### LightCone7 Tutorial Part III - How Things are Computed

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In Part I and Part II of this mini-series, we have briefly discussed…

### Complex and Irrational Exponents for the Layman

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This Insight is part of our "Young Authors" series, where talented…

### LightCone7Combo Tutorial Part II - Charts

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Part I dealt with the basic user interface of LightCone7Combo.…

### What Are Eigenvectors and Eigenvalues?

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Two important concepts in Linear Algebra are eigenvectors…

### LightCone7Combo Tutorial Part I

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LightCone 7 Combo is a versatile tabulating/charting cosmological…

### Partial Fractions Decomposition

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Partial fractions decomposition is an algebraic technique that can…

### Frequently Made Errors in Climate Science - The Greenhouse Effect

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1.What is meant by "The Greenhouse Effect"? Many gases, such…

### Solving Nonhomogeneous Linear ODEs using Annihilators

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My previous Insights article, Solving Homogeneous Linear ODEs…

### Solving Homogeneous Linear ODEs using Annihilators

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In this Insights article we'll look at a limited class of ordinary…

### Matrix Representations of Linear Transformations

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Let X and Y be finite-dimensional vector spaces. Let ##T:X\to…

### Simple Python Debugging with Pdb: Part 2

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This Insight article is the continuation of the first article, Simple…

### Simple Python Debugging with Pdb: Part 1

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I'm pretty new with Python, so I was looking around for some…

### Informal Introduction to Cardinal Numbers

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Cardinal numbers We will now give an informal introduction to…

### Is There a Rigorous Proof Of 1 = 0.999...?

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Yes. First, we have not addressed what 0.999... actually means.…

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### A Short Proof of Birkhoff's Theorem

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Birkhoff's theorem is a very useful result in General Relativity,…

### Frequently Made Errors in Heat: Elementary Level

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1. Heat, Work, Internal Energy and Kinetic Energy "If heat is…

### Errors in Probability: Continuous and Discrete Distributions

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1. Classifying as discrete, continuous or mixed These statements…

### Frequently Made Errors: Pseudo and Resultant Forces

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1. Real versus Fictitious Pseudo, or "fictitious",…

### Why Renormalisation Needs a Cutoff

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This is a follow on from my paper explaining renormalisation.…

### Frequently Made Errors in Mechanics: Springs

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1. Springs in Series "A spring of constant ##k_1##…

### Frequently Made Errors in Probability: Conditionals in Natural Language

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1. Turning a verbal condition into Algebra An actual…

### Frequently Made Errors in Mechanics: Momentum and Impacts

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An impact is an impulse (change of momentum)…

### Frequently Made Errors in Mechanics: Hydrostatics

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1. Archimedes' Principle X "When a body is placed…

### Conceptual Difficulties in the Roles of Variables

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1. Variables and Constants When is a constant not a constant? …

### A Partial "Derivation" of Gauss's Law

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Gauss's law was formulated by Carl Friedrich Gauss in 1835. It…

### Frequently Made Errors in Equation Handling

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1. Algebra versus Arithmetic When numerical values…

### Frequently Made Errors in Mechanics: Kinematics

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Kinematics is the subset of dynamics…

### Frequently Made Errors in Mechanics: Moments

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The term "moment" is used in various ways in Physics…

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What Is The Issue With Renormalisation If you have an interest…

### Misconceiving Mutual Inductance Coefficients

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A commonly used formula for mutual inductance M between…

### Frequently Made Errors in Mechanics - Friction

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1. Direction of the normal Definition: The normal…

### A Continuous, Nowhere Differentiable Function: Part 2

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This is Part 2 of a series of articles in which the goal is to…

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### Visualizing the 2-D Particle in a Box

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The particle in a box is a staple of entry-level Quantum Mechanics classes…

### A Continuous, Nowhere Differentiable Function: Part 1

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When studying calculus, we learn that every differentiable function…

### Understanding Entropy and the 2nd Law of Thermodynamics

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Introduction The second law of thermodynamics and the associated…