Daily Archives: August 25, 2026

15 posts
Before Physics

Completing the Square – Deriving the Perfect Square Form of a Quadratic

The Ultimate Crash Course for STEM Majors This is nothing more than a free preview/sample of The Ultimate Crash Course for STEM Majors. Visit AuthorJonD.com for books, lessons, educational resources, and additional STEM material. Complete the Square $$x^2-\frac{1}{2}x-\frac{3}{16}=0,\qquad 16x^2-8x-3=0$$ Complete the Square $$ax^2+b+c=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right)=0 \Rightarrow a\left(x^2+\frac{b}{a}x+\frac{c}{a}+0\right)=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a} +\left[\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2\right]\right)=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a} +\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2\right)=0$$ […]

Ultimate Cheat Sheet

About the Author – Jonathan David

Free Preview of The Ultimate Crash Course for STEM Majors This page is nothing more than a free preview of The Ultimate Crash Course for STEM Majors. Visit AuthorJonD.com to explore the Crash Course series, books, lessons, and additional educational material. You can also check out my fiction, books, stories, […]

Math Monthly

Operator Notation for Derivatives and PDEs – Single Variable and Multivariable Differentiation

Free Preview of The Ultimate Crash Course for STEM Majors This lesson is nothing more than a free preview of The Ultimate Crash Course for STEM Majors. The Crash Course series provides worked mathematics and physics examples designed to strengthen calculus, differential equations, physics, engineering mathematics, and advanced STEM problem-solving […]