Master Math with Clear, Step-by-Step Instruction
Welcome to Understand the Math, a channel dedicated to clear, accurate, and thoughtfully structured mathematics instruction for high school students, college students, and lifelong learners.
I’m Cheryl Hile, Ph.D. in Engineering Science and Applied Mathematics, with over 25 years of university teaching experience. Videos focus on building real understanding through worked examples and step-by-step problem-solving across algebra, trigonometry, precalculus, calculus, linear algebra, and ordinary differential equations.
Free guided notes are linked in each video description to support practice and review.
📌 Subscribe for structured math instruction designed to build real understanding and confidence.
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
5 days ago | [YT] | 2
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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 week ago | [YT] | 2
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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 week ago | [YT] | 6
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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.
2 weeks ago | [YT] | 3
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Understand The Math
Getting ready for a math exam soon?
Here’s a simple reminder that can make a big difference: how you study matters just as much as what you study.
If you missed it, I recently shared a video that walks through 5 practical strategies to help you feel more organized, focused, and confident on exam day — no matter which math class you’re taking.
If you want a clear plan for reviewing notes, organizing formulas, and practicing problems effectively, this video can help.
🎥 Watch here: https://youtu.be/XWi9SPXhaaw
Which part of math exam prep do you find most helpful—reviewing notes, memorizing formulas, or working practice problems?
7 months ago | [YT] | 1
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Understand The Math
Starting your week with Calculus 1 review?
Here’s a set of resources many students use to feel more confident before finals.
This review series walks through exam-style practice problems with clear, step-by-step solutions. Each video focuses on one topic at a time, making it easy to review limits, derivatives, integrals, and applications throughout the week.
Exam Review Playlist:
www.youtube.com/playlist?list...
Free Practice Problem PDF:
www.understandthemath.com/calculus1-exam-review
7 months ago | [YT] | 0
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Understand The Math
Cosine is positive in Quadrant II.
See the explanation in this example: https://youtu.be/lFpbswAA3a0
7 months ago | [YT] | 1
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Understand The Math
Reviewing Calculus 1 Example Problems? 📘
This playlist features step-by-step solutions to key Calculus 1 problems, organized by topic. Each video focuses on one example at a time so you can review core concepts and strengthen your problem-solving skills alongside your main lessons.
Topics covered include:
• Limits and continuity
• Derivative rules and applications
• Curve sketching, related rates, and optimization
• Integrals and substitution
• Applications of integrals such as area, volume, and average value
Example Problems Playlist:
www.youtube.com/playlist?list...
Free Guided Notes 📝
www.understandthemath.com/calculus-1
7 months ago | [YT] | 0
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Understand The Math
Preparing for Your Linear Algebra Exam?
Review essential concepts and problem types with my Linear Algebra Exam Review Course — each video walks through step-by-step examples commonly tested in university-level linear algebra.
Topics Included:
• Linear systems
• Linear transformations
• Matrix algebra
• Determinants
• Vector spaces
• Eigenvalues and eigenvectors
• Orthogonality and least squares
Exam Review Playlist:
www.youtube.com/playlist?list...
Free Guided Notes:
www.understandthemath.com/linear-algebra-exam-revi…
7 months ago | [YT] | 0
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Understand The Math
🔢 Building Confidence in Math—One Step at a Time! 🔢
Math isn’t about memorization—it’s about understanding the “why” behind the concepts. Whether you're working through algebra, trigonometry, calculus, or linear algebra every concept connects to a bigger picture.
💡 Keep pushing forward, keep practicing, and most importantly—keep believing in yourself!
What math topic are you currently working on? Drop a comment below! 👇
#UnderstandTheMath #MathConfidence #KeepLearning #Algebra #Trigonometry #Calculus #LinearAlgebra
1 year ago | [YT] | 0
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