Trigonometric Identities
Trigonometric identities are equations involving trig functions that hold true for every valid value of the variable. You'll use them constantly, whether you're simplifying expressions, solving equations, or proving other…
Mathematics
Whole Numbers
Whole numbers are one of the first building blocks you encounter in mathematics, yet they show up everywhere, from counting everyday objects to performing complex calculations. In this guide, you…
Supremum and Infimum
Supremum and infimum are two of the most fundamental concepts you will encounter in real analysis. They generalize the familiar ideas of maximum and minimum to situations where a set…
Function: Notations and Rules
TLDR; A function is a relation where every input maps to exactly one output. This page covers the formal definition, standard notation like \( f(x) \), and the concepts of…
Set
What is a Set in Mathematics? A set is a well-defined collection of distinct objects. If you've ever grouped items together and referred to them as one thing, you already…
Circumcenter of a Triangle: Definition, Types and Examples
Every triangle has a special point where you can place a compass and draw a perfect circle through all three vertices. That point is called the circumcenter, and finding it…
Significant Figures: Definition, Usage and Examples
Significant Figures: Definition, Usage and Examples. A comprehensive guide with practical insights and actionable advice.
Zero of a Function
The zero of a function is the input value that makes the output equal to zero. You'll encounter this concept constantly, from basic algebra through calculus and beyond. Every time…
Best Time Saving Mathematics Formulas & Theorems
Here's the deal: mathematics has thousands of formulas, but only a handful will genuinely change how fast you solve problems. After years of teaching and competitive math, I've compiled the…
How to convert Integral Equations into Differential Equations?
Step-by-step guide to convert integral equations into differential equations?. Clear instructions with practical tips for getting it done right.
Important Definitions in Functional Analysis
Functional Analysis is where linear algebra meets topology. It's the study of infinite-dimensional spaces—and if that sounds abstract, here's why you should care: it's the mathematical backbone of quantum mechanics,…
How to change Differential Equations into Integral Equations?
This post explains the basic method of converting an integral equation into a corresponding differential equation.