Understand The Math

Working on integration by parts? Here’s a cheat sheet with the formula, steps to follow, and the ILATE shortcut for choosing (u).
Want to see integration by parts in action? In this video, I work through 6 examples step by step and also show the tabular integration shortcut:
https://youtu.be/LvJ-N6A7FeU
Save this cheat sheet for when you need it! 📚

1 day ago | [YT] | 3

Understand The Math

Need help remembering which trig functions are positive in each quadrant?

“All Students Take Calculus” makes it easy:

Quadrant I: All
Quadrant II: Sine
Quadrant III: Tangent
Quadrant IV: Cosine

🎥 Want to see how it works? Watch the full explanation:
https://youtu.be/lFpbswAA3a0

1 week ago | [YT] | 1

Understand The Math

Can every matrix be written as the product of three simpler matrices?

Yes! The Singular Value Decomposition (SVD) writes any matrix as
A = UΣVᵀ.

This quick reference summarizes what each matrix represents and how they fit together. Save it for future reference, then watch the full lesson for a complete step-by-step example.

▶️ https://youtu.be/f8DVtPvqtwc

2 weeks ago | [YT] | 0

Understand The Math

📌 Graphing Transformations in 4 Steps
1️⃣ Graph the parent function.2️⃣ Scale the graph.3️⃣ Translate the graph.4️⃣ Reflect the graph.
Following the same order every time makes graphing transformations much easier.
🎥 Watch the full lesson here: https://youtu.be/DfpTz2oXYpo
📌 Save this for your next algebra or precalculus exam!

3 weeks ago | [YT] | 3

Understand The Math

Subspaces can be one of the trickiest topics in an introductory Linear Algebra course.
This quick reference summarizes the definition, the three subspace conditions, and several common examples.
📌 Save it for later when you're studying!
For a complete explanation of vector spaces and subspaces, watch the lesson here: https://youtu.be/Niz4RbwxOfw

4 weeks ago | [YT] | 5

Understand The Math

Calculus tip! The chain rule is all about taking the derivative of the outside function and multiplying by the derivative of the inside function. Here's a quick reference with formulas and examples.
Watch the full lesson here: https://youtu.be/mnfX_i2LK1A

1 month ago | [YT] | 2

Understand The Math

Second-order differential equations don't have to be overwhelming.

This graphic summarizes the three possible cases based on the discriminant of the characteristic equation and the corresponding general solution for each.

📌 Save this for your next quiz or exam.

If you'd like to see these ideas explained step by step with examples, here's the full lesson: https://youtu.be/9H6IfrGLJpE

1 month ago | [YT] | 2

Understand The Math

Sinusoidal functions don't have to be confusing.

This graphic highlights the four key features you need to identify from

y = A sin(B(x − C)) + D

✔️ Amplitude
✔️ Period
✔️ Phase Shift
✔️ Midline

📌 Save this for your next quiz or exam.

Want to learn how to graph sinusoidal functions step by step? Watch the full lesson here: https://youtu.be/62bqzy9qtB0

1 month ago | [YT] | 2

Understand The Math

One-to-One vs. Onto Transformations

These are two of the most important—and often most challenging—concepts in linear algebra.

Here's a quick visual cheat sheet that summarizes the key differences. Save it for when you're studying! 📚

1 month ago | [YT] | 6

Understand The Math

🎉 The redesigned Understand The Math website is live!
It's now easier to find the math course you need, with free videos, guided notes, and study resources organized by course.

1 month ago | [YT] | 3