# 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

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Introduction There are a  number of posts on PF involving…

### Make Units Work for You

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

### A Journey to The Manifold SU(2): Representations

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

### Further Sums Found Through Fourier Series

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

### The Pantheon of Derivatives - Part V

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Important Theorems - biased, of course Implicit…

### The Pantheon of Derivatives - Part IV

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Lie Derivatives A Lie derivative is in general the…

### The Pantheon of Derivatives - Part III

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Some Topology Whereas the terminology of vector…

### The Pantheon of Derivatives - Part II

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

### The Pantheon of Derivatives - 5 Part Series

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Differentiation in a Nutshell I want to gather the…

### Trick to Solving Integrals Involving Tangent and Secant

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This little trick is used for some integration problems involving…

### 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)…

### Partial Differentiation Without Tears

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

### Solving the Cubic Equation for Dummies

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Everybody learns the "quadratic formula" for solving equations…

### Omissions in Mathematics Education: Gauge Integration

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

### Explaining the General Brachistochrone Problem

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

### Some Misconceptions on Indefinite Integrals

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Integration is an incredibly useful technique taught in all calculus…

### Mathematical Irrationality for Dummies

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

### Complex and Irrational Exponents for the Layman

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

### What Are Eigenvectors and Eigenvalues?

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Two important concepts in Linear Algebra are eigenvectors…

### Partial Fractions Decomposition

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Partial fractions decomposition is an algebraic technique that can…

### 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…

### 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.…

### Errors in Probability: Continuous and Discrete Distributions

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

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

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1. Turning a verbal condition into Algebra An actual…

### Conceptual Difficulties in the Roles of Variables

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

### 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…

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

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When studying calculus, we learn that every differentiable function…