French translation of
jacobian
is
jacobien
Tap once to copy the translated word
Meaning of "jacobian" in English
The term "jacobian" refers to a mathematical concept used primarily in calculus and differential geometry. It is a matrix of all first-order partial derivatives of a vector-valued function. In simpler terms, the Jacobian matrix represents the best linear approximation of a function near a given point. The determinant of the Jacobian is crucial in various applications, such as analyzing critical points and calculating transformations in multivariable calculus and physics.
Meaning of "jacobien" in French
In French, "jacobien" refers to the same mathematical concept as its English counterpart. It describes a matrix of partial derivatives that help analyze functions of several variables. The Jacobian, or "jacobien," is essential in studying transformations and approximations in multivariable calculus. Its determinant is particularly useful in tasks such as understanding the behavior of dynamical systems and ensuring proper coordinate transformations.
Pronunciation of "jacobian" in English
Phonetic Transcription: /dʒəˈkoʊ.bi.ən/
Pronunciation Variations: In different English-speaking regions, the pronunciation remains largely consistent, with slight variations in accent. For instance, the emphasis on certain syllables might differ slightly between American and British English.
Pronunciation of "jacobien" in French
Phonetic Transcription: /ʒa.kɔ.bjɛ̃/
Pronunciation Variations: The pronunciation of "jacobien" is consistent across French-speaking regions, though the accent can vary slightly based on local dialects. Generally, the nasality and articulation of the vowels are characteristic of the French language.
Sentence examples in English and translation to French
- The Jacobian matrix is critical in evaluating the nonlinear system. - La matrice jacobienne est cruciale pour évaluer le système non linéaire.
- Understanding the Jacobian helps in predicting system behavior. - Comprendre le jacobien aide à prédire le comportement du système.
- Engineers often calculate the Jacobian for control systems. - Les ingénieurs calculent souvent le jacobien pour les systèmes de contrôle.
- The determinant of the Jacobian indicates function behavior. - Le déterminant du jacobien indique le comportement de la fonction.
- The Jacobian provides insights into dynamical system changes. - Le jacobien fournit des informations sur les changements de systèmes dynamiques.
- Calculating the Jacobian is fundamental in robotics. - Calculer le jacobien est fondamental en robotique.
- The accuracy of the Jacobian impacts simulation results. - La précision du jacobien impacte les résultats de simulation.
- Mastery of the Jacobian is crucial for advanced calculus. - La maîtrise du jacobien est cruciale pour le calcul avancé.
- The Jacobian determines the stability of equilibria. - Le jacobien détermine la stabilité des équilibres.
- In optimization, the Jacobian helps refine algorithms. - En optimisation, le jacobien aide à affiner les algorithmes.
Synonyms, antonyms, and similar words for "jacobian" in English
Synonyms: derivation matrix, differential matrix, gradient matrix, transformation matrix.
Antonyms: -
Similar Words: determinant, derivative, matrix, calculus, vector field.
Synonyms, antonyms, and similar words for "jacobien" in French
Synonyms: matrice de dérivée, matrice différentielle, matrice de gradient, matrice de transformation.
Antonyms: -
Similar Words: déterminant, dérivée, matrice, calcul différentiel, champ vectoriel.
Disclaimer: These examples may contain sensitive content that does not reflect the opinions or policies of Translate.com, or its company Translate LLC. We welcome feedback: report an example sentence to our team.