LaTeX
\nabla\cdot\mathbf F=\sum_i\frac{\partial F_i}{\partial x_i}Variables
- F: vector field
- Fᵢ: components
How to use this formula
Measures local source or sink strength of a vector field.
Important notes
- Coordinate-specific forms differ outside Cartesian coordinates.
Quick example
For F=(x,y), divergence is 2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Coordinate-specific forms differ outside Cartesian coordinates.
- For the Divergence, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Divergence, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- Preserve matrix order and verify dimension compatibility; multiplication and inversion are not generally commutative or always defined.
Worked example
For F=(x,y), divergence is 2.
Common mistakes
- When copying Divergence, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not apply a differentiation or integration rule outside its domain or omit endpoint, continuity, or constant-of-integration checks.
Continue the workflow
Use Divergence in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\nabla\cdot\mathbf F=\sum_i\frac{\partial F_i}{\partial x_i}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Calculus Volume 1OpenStax, Rice University — Reviewed limits, derivatives, integrals, and foundational calculus formulas.
Frequently asked questions
What is the Divergence used for?
Measures local source or sink strength of a vector field.
Can I copy this formula as LaTeX?
Yes. Copy \nabla\cdot\mathbf F=\sum_i\frac{\partial F_i}{\partial x_i} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.