20 Best Calculus Books [Best Sellers Included]
Calculus textbooks can make or break your understanding of the subject. I struggled with calculus the first time around because…
Calculus
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I…
The Area of a Disk
The area of a disk is pi times radius squared. You memorized this in middle school. But do you know…
Triangle Inequality
The triangle inequality sounds obvious. No side of a triangle can be longer than the other two sides combined. But…
Numbers – The Basic Introduction
Numbers are the alphabet of mathematics. But here's what most people never learn: all the complex numbers you encounter, from…
Everywhere Continuous, Nowhere Differentiable: The Weierstrass Function and Why It Matters
In 1872, Weierstrass presented a function that's continuous everywhere but differentiable nowhere. It shattered the assumption that smooth curves are…
Free Online Calculus Text Books
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have…
D’Alembert’s Ratio Test for Convergence of Series
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges.…
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Dirichlet theorem connects the Gamma and Beta functions to evaluate complex multiple integrals. Liouville extended it further, making it…
Derivative of x squared is 2x or x ? Where is the fallacy?
Here's a mathematical fallacy that trips up even sharp students. Can you prove that the derivative of x squared is…
Solving Ramanujan’s Puzzling Problem
Ramanujan's nested radical problem looks impossible at first glance. Infinitely many nested square roots, each multiplied by increasing integers. How…