Learn the language of change
A visual, interactive workbook
Differential equations stop feeling like a bag of tricks when you can read what an equation says about motion. This book trains that reading skill first, then turns it into reliable solution habits.
What you will learn to do
Most courses organize differential equations by chapter titles. Problems rarely arrive with their chapter title attached. This workbook organizes your attention around four questions:
Name the state and its units.
Read signs, factors, and feedback.
Choose a method from structure.
Check units, shape, and substitution.
By the end, you should be able to move among four representations of the same model:
The workout rhythm
Each chapter repeats the same deliberate sequence.
- Notice. Predict from a picture, a story, or the equation's shape.
- Name. Learn one small piece of mathematical language.
- Work. Study a fully explained example.
- Fade. Complete a similar example with fewer steps supplied.
- Choose. Mix the new method with older ones so that you must identify the method yourself.
- Check. Test the result against the original equation and its expected behavior.
Your practice contract
Make a prediction before touching the algebra. Write one line for every transformation. Open a solution only after committing to an attempt. When an answer is wrong, name the first line where the reasoning changed course.
What you need
You should be comfortable with derivatives, antiderivatives, exponentials, logarithms, and basic algebra. Chapter 9 introduces the small amount of linear algebra it needs. A calculator helps with arithmetic, but every central idea works without special software.
No interactive lab sends data anywhere. Checkpoints stay in your browser. You can clear them from the button below.
No checkpoints completed yet.
A two-minute preflight
Try these without notes. The point is to choose a starting pace, not to earn a score.
1. If \(y'(t)<0\) on an interval, what must the graph of \(y\) do there?
2. Which derivative rule recognizes \(e^{2t}y' + 2e^{2t}y\)?
If either question felt unfamiliar, work straight through Parts I and II. If both felt immediate, skim Chapter 1 and spend more time on the integrated problems.