Differential Equations › Section A · Basic concepts › Topic A.2
Direction fields
A first-order equation tells you the slope of its solutions at every point, so you can draw them before you can solve them. A direction field turns the equation into a picture that shows how solutions behave and how that behaviour depends on where they start.
In this topic
- A picture before a formula
- Building a direction field
- Integral curves
- Worked example: a field without t
- Isoclines
- Worked example: isoclines of a linear equation
- Fields with and without t
- Worked example: a drug infusion
- What a field can and cannot tell you
- Common mistakes to avoid
- Key takeaways
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