# Mathematics Tutorials

### 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,…

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

/
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…

### The Pantheon of Derivatives - Part V

/
Important Theorems - biased, of course Implicit…

### 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…

### Using the Fourier Series To Find Some Interesting Sums

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

### 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…

### Omissions in Mathematics Education: Gauge Integration

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

### 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…

### Irrationality for Dummies

/
On one of my restless wanderings around the Internet, I came…

### Complex and Irrational Exponents for the Layman

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

### What Are Eigenvectors and Eigenvalues?

/
Two important concepts in Linear Algebra are eigenvectors…

### Partial Fractions Decomposition

/
Partial fractions decomposition is an algebraic technique that can…

### Solving Nonhomogeneous Linear ODEs using Annihilators

/
My previous Insights article, Solving Homogeneous Linear ODEs…

### Solving Homogeneous Linear ODEs using Annihilators

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

### Matrix Representations of Linear Transformations

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

### Informal Introduction to Cardinal Numbers

/
Cardinal numbers We will now give an informal introduction to…

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

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

### Frequently Made Errors in Probability - Continuous and Discrete Distributions

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

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

/
1. Turning a verbal condition into Algebra An actual…

### Conceptual Difficulties in the Roles of Variables

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

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

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

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

/
When studying calculus, we learn that every differentiable function…