Title: Outils mathématiques : Analyse vectorielle

Q: Notation nabla
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘∇’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘vec’, ‘children’: [{‘func’: ‘context’}, {‘func’: ‘context’}, {‘func’: ‘context’}]}]}}

Q: Gradient
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘∇’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘vec’, ‘children’: [{‘func’: ‘context’}, {‘func’: ‘context’}, {‘func’: ‘context’}]}]}}

Q: À quoi s’applique le gradient ? Que renvoie-t-il ?
A: Le gradient s’applique aux champs scalaires et renvoie un champ vectoriel.

Q: Divergence
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘text’, ‘text’: ‘div ‘}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘∇’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘context’}]}}

Q: À quoi s’applique la divergence ? Que renvoie-t-elle ?
A: La divergence s’applique aux champs vectoriels et renvoie un champ scalaire.

Q: Théorème d’Ostrogradski
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘∭’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘V’}}, {‘func’: ‘space’}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘text’, ‘text’: ‘div ‘}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘h’, ‘amount’: ‘0.16em’, ‘weak’: True}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘d’}, ‘styles’: ‘..’}}, {‘func’: ‘symbol’, ‘text’: ‘V’}]}}]}}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘∯’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘S’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘h’, ‘amount’: ‘0.16em’, ‘weak’: True}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘d’}, ‘styles’: ‘..’}}, {‘func’: ‘symbol’, ‘text’: ‘S’}]}}]}}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}]}}

Q: Rotationnel
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘∇’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘∧’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘vec’, ‘children’: [{‘func’: ‘sequence’, ‘children’: [{‘func’: ‘context’}, {‘func’: ‘symbol’, ‘text’: ‘−’}, {‘func’: ‘context’}]}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘context’}, {‘func’: ‘symbol’, ‘text’: ‘−’}, {‘func’: ‘context’}]}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘context’}, {‘func’: ‘symbol’, ‘text’: ‘−’}, {‘func’: ‘context’}]}]}]}}

Q: À quoi s’applique le rotationnel ? Que renvoie-t-il ?
A: Le rotationnel s’applique aux champs vectoriels et renvoie un champ vectoriel.

Q: Théorème de Stockes
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘∯’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘S’}}, {‘func’: ‘space’}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘h’, ‘amount’: ‘0.16em’, ‘weak’: True}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘d’}, ‘styles’: ‘..’}}, {‘func’: ‘symbol’, ‘text’: ‘S’}]}}]}}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘∮’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘C’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘h’, ‘amount’: ‘0.16em’, ‘weak’: True}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘d’}, ‘styles’: ‘..’}}, {‘func’: ‘symbol’, ‘text’: ‘l’}]}}]}}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}]}}

Q: Champ irrotationnel
A: Champ dont le rotationnel est nul.

Q: Comment peut-on écrire un champ irrotationnel ?
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘0’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘⇔’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘∃’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘|’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}]}}

Q: Divergence d’un produit vectoriel
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘text’, ‘text’: ‘div ‘}}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘∧’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘B’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}]}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘B’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘−’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘B’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}]}}

Q: Laplacien scalaire
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘Δ’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘text’, ‘text’: ‘div ‘}}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘f’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}]}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘context’}]}}

Q: À quoi s’applique le laplacien scalaire ? Que renvoie-t-il ?
A: Le laplacien scalaire s’applique aux champs scalaires et renvoie un champ scalaire.

Q: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘symbol’, ‘text’: ‘⋅’}}, {‘func’: ‘space’}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}]}}
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘.’}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘x’}}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘y’}}, {‘func’: ‘space’}, {‘func’: ‘context’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘+’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘z’}}, {‘func’: ‘space’}, {‘func’: ‘context’}]}}

Q: À quoi s’applique l’opérateur ? Que renvoie-t-il ?
A: L’opérateur s’applique aux champs scalaires et vectoriels, et renvoie respectivement un scalaire et un vecteur.

Q: Laplacien vectoriel
A: {‘func’: ‘equation’, ‘block’: True, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘accent’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘Δ’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘grad ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘text’, ‘text’: ‘div ‘}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}]}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘−’}, {‘func’: ‘space’}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘lr’, ‘body’: {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘(‘}, {‘func’: ‘class’, ‘class’: ‘unary’, ‘body’: {‘func’: ‘equation’, ‘block’: False, ‘body’: {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘text’, ‘text’: ‘rot ‘}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}}}, {‘func’: ‘space’}, {‘func’: ‘accent’, ‘base’: {‘func’: ‘styled’, ‘child’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘styles’: ‘..’}, ‘accent’: ‘⃗’}, {‘func’: ‘symbol’, ‘text’: ‘)’}]}}]}, {‘func’: ‘space’}, {‘func’: ‘symbol’, ‘text’: ‘=’}, {‘func’: ‘space’}, {‘func’: ‘vec’, ‘children’: [{‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘Δ’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘x’}}]}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘Δ’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘y’}}]}, {‘func’: ‘sequence’, ‘children’: [{‘func’: ‘symbol’, ‘text’: ‘Δ’}, {‘func’: ‘space’}, {‘func’: ‘attach’, ‘base’: {‘func’: ‘symbol’, ‘text’: ‘A’}, ‘b’: {‘func’: ‘symbol’, ‘text’: ‘z’}}]}]}]}}

Q: À quoi s’applique le laplacien vectoriel ? Que renvoie-t-il ?
A: Le laplacien vectoriel s’applique aux champs vectoriels et renvoie un champ vectoriel.