BitWithBite
Mathematics Worksheet
🌊 Divergence
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After this worksheet you can
Compute divergence div F = ∂P/∂x + ∂Q/∂y.Interpret divergence as a source (spreading) or sink (converging).Recognise divergence-free (incompressible) fields.Extend the idea to three-dimensional fields.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1div F for F = (4x, 5y) = ?
2div F for F = (x2, y3) = ?
3div F for F = (y2, x2) = ?
4div F for F = (x, y, z) = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5For F = (P, Q), div F = .
6div F for F = (4x, 5y) = .
7Find the divergence of F = (4x, 5y).
8Find the divergence of F = (x2, y3).
9Find the divergence of F = (y2, x2).
🚀 Section C · Challenge ● CHALLENGE 5
10Find the divergence of F = (x, y, z).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-C 2-A 3-A 4-C | 5 ∂P/∂x + ∂Q/∂y 6 9 7 = 9 8 = 2x + 3y2 9 = 0 | 10 = 3