Math Tutorials

Here contain all the math tutorials for all mathematics areas. These are technical how-to articles that focus on teaching you a specific skill or how to solve a specific problem. From basic algebra to advanced calculus. Self study and classroom strategy. Learn something new today!

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): 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…

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…

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…

Mathematical 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.…

Errors in Probability: Continuous and Discrete Distributions

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

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? …
differentiable function 2

A Continuous, Nowhere Differentiable Function: Part 2

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

A Continuous, Nowhere Differentiable Function: Part 1

When studying calculus, we learn that every differentiable function…