Before Physics

5 posts

Exponential and Logarithmic Derivatives

The Ultimate Crash Course for STEM Majors This is nothing more than a free preview/sample of The Ultimate Crash Course for STEM Majors. This lesson reviews exponential and logarithmic formulas, inverse functions, logarithmic derivatives, exponential derivatives, and the derivation of the exponential derivative formula. Visit AuthorJonD.com for books, lessons, educational […]

Vector Notations in Physics

The Ultimate Crash Course for STEM Majors This is nothing more than a free preview/sample of The Ultimate Crash Course for STEM Majors. This lesson covers vector notation, unit vectors, scalar and vector functions, higher-dimensional functions, and introductory vector differentiation and integration. Visit AuthorJonD.com for books, lessons, educational resources, and […]

Plotting Vectors and Summation

The Ultimate Crash Course for STEM Majors This is nothing more than a free preview/sample of The Ultimate Crash Course for STEM Majors. This lesson introduces plotting vectors, repositioning vectors at the origin, vector components, and the basic method used to find a resultant vector. Visit AuthorJonD.com for books, lessons, […]

Solving Equations and Checking Your Work

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. Solving Equations and Checking Your Work Solve for $x$, $$ \frac{(xyz)^{\frac{a}{3}}}{abc}=\sqrt{axy}. $$ Can you solve for […]

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 $$ax^2+b+c=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right)=0 \Rightarrow a\left(x^2+\frac{b}{a}x+\frac{c}{a}+0\right)=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a} +\left[\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2\right]\right)=0$$ $$a\left(x^2+\frac{b}{a}x+\frac{c}{a} +\left(\frac{b}{2a}\right)^2-\left(\frac{b}{2a}\right)^2\right)=0$$ […]