Free step-by-step math lessons with guided notes to help you truly understand math.
Welcome to Understand The Math, where you'll find clear explanations, worked examples, and free guided notes designed to help you build confidence and succeed in math.
Whether you're studying algebra, trigonometry, precalculus, calculus, linear algebra, or differential equations, you'll find lessons that focus on building real understanding, not just memorizing formulas.
Created by Dr. Cheryl Hile, a former Penn State mathematics professor with more than 25 years of university teaching experience and a Ph.D. in Engineering Science and Applied Mathematics.
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Understand The Math
Do you remember the Product Rule?
The Product Rule is used to find the derivative of a product of two functions. In this short, I explain what the Product Rule is and work through a quick example showing exactly how to use it.
If you’re learning derivatives in Calculus 1 or AP Calculus AB, this is an important differentiation rule to know.
Watch the short here: youtube.com/shorts/jkFciKJuVl...
#ProductRule #Calculus #Derivatives
11 hours ago | [YT] | 1
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Understand The Math
Need a quick Product Rule refresher? Here’s a cheat sheet with the formula and worked examples to help you remember how to differentiate the product of two functions.
The Product Rule:
f(x)g′(x) + g(x)f′(x)
Save this for your next Calculus 1 or AP Calculus AB review!
#ProductRule #Derivatives #Calculus #Calculus1 #APCalculus
2 days ago | [YT] | 4
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Understand The Math
Do you know the three conditions for continuity?
For a function to be continuous at a point, all three conditions must be true:
1. f(a) exists
2. lim x→a f(x) exists
3. f(a) = lim x→a f(x)
If even one condition fails, the function is not continuous at x = a.
Swipe through the images to see examples of each condition failing—and what happens when all three conditions are satisfied. ➡️
This is an important concept to understand when studying limits and continuity in Calculus 1.
#Continuity #Calculus #Calculus1 #Limits #MathHelp
1 week ago | [YT] | 2
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Understand The Math
One of the hardest parts of integration is deciding which technique to try.
In this video, I work through 12 integration practice problems step by step, using a variety of techniques so you can see how to recognize which approach to use.
▶️ Watch here: https://youtu.be/hIzE5NKe_kY
Which integration technique gives you the most trouble?
#Calculus #Integration #Calculus2 #MathHelp
1 week ago | [YT] | 0
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Understand The Math
Degrees or radians — how do you convert between them? 🔄
The key relationship is:
360° = 2π radians
From there, we get the two conversion rules:
➡️ Degrees to radians: multiply by π/180
➡️ Radians to degrees: multiply by 180/π
In this video, I explain where these conversion factors come from and work through examples step by step.
🎥 Watch the full lesson here:
https://youtu.be/95n8NjYVI-g
#Trigonometry #Degrees #Radians #LearnMath #MathHelp
2 weeks ago | [YT] | 2
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Understand The Math
Complementary or supplementary? 📐
These two terms are easy to mix up, but the difference comes down to the sum of the angles:
Complementary angles add to 90°.
Supplementary angles add to 180°.
An easy way to remember: complementary angles complete a right angle, while supplementary angles complete a straight angle.
Save this for a quick geometry review!
#ComplementaryAngles #SupplementaryAngles #Geometry #LearnMath #MathHelp
2 weeks ago | [YT] | 3
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Understand The Math
Tabular integration is a shortcut that organizes the derivatives, integrals, and alternating signs to make repeated integration by parts much easier.
Watch the full lesson here: https://youtu.be/gAbh1cXfqug
2 weeks ago | [YT] | 5
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Understand The Math
Need help with parabolas?
Learn about the vertex, focus, directrix, and axis of symmetry—and how to write the equation of a parabola.
Watch the full lesson here: https://youtu.be/l_OSqvr_sgQ
3 weeks ago | [YT] | 4
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Understand The Math
What is Singular Value Decomposition?
SVD factors a matrix into three matrices: U, Σ, and Vᵀ. This graphic shows the decomposition and the role each matrix plays.
Watch my step-by-step example to see how SVD works: https://youtu.be/f8DVtPvqtwc
3 weeks ago | [YT] | 1
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Understand The Math
Need to find the midpoint or distance between two points?
Here are the midpoint and distance formulas, along with an example of each.
Save this for later
3 weeks ago | [YT] | 3
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