deriitive5

The Pantheon of Derivatives - Part V

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  Important Theorems - biased, of course Implicit…
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…
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)…
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…
omissionguage

Omissions in Mathematics Education: Gauge Integration

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

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…
irrationalnumbers

Irrationality for Dummies

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

Complex and Irrational Exponents for the Layman

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

What Are Eigenvectors and Eigenvalues?

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Two important concepts in Linear Algebra are eigenvectors…
partialfractions

Partial Fractions Decomposition

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Partial fractions decomposition is an algebraic technique that can…
ODE2

Solving Nonhomogeneous Linear ODEs using Annihilators

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My previous Insights article, Solving Homogeneous Linear ODEs…
ODE1

Solving Homogeneous Linear ODEs using Annihilators

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

Matrix Representations of Linear Transformations

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

Informal Introduction to Cardinal Numbers

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Cardinal numbers We will now give an informal introduction to…
999

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

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

Frequently Made Errors in Probability - Continuous and Discrete Distributions

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

Frequently Made Errors in Probability - Conditionals in Natural Language

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

Conceptual Difficulties in the Roles of Variables

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1. Variables and Constants When is a constant not a constant? …
differentiable function 2

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…
differentiable function

A Continuous, Nowhere Differentiable Function: Part 1

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When studying calculus, we learn that every differentiable function…