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Lecture# Geometric Interpretation of Jacobian

Description

This lecture covers the transformation of coordinates in two dimensions, the Jacobian matrix, and examples of illicit transformations. It explains the geometric interpretation of the Jacobian, conditions for existence of inverse transformations, and the quality of transformations. The slides illustrate deformed geometrically finite elements, negative Jacobian values, and special cases of illegal transformations.

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In course

Instructor

ME-372: Finite element method

L'étudiant acquiert une initiation théorique à la méthode des éléments finis qui constitue la technique la plus courante pour la résolution de problèmes elliptiques en mécanique. Il apprend à applique

Related concepts (26)

Related lectures (2)

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In mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent history. Although rings have more structure than groups, the theory of finite rings is simpler than that of finite groups.

Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when p is a prime number. The order of a finite field is its number of elements, which is either a prime number or a prime power.

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Explores the Jacobian matrix for geometrically finite elements in the Finite Element Method.

Covers propositional logic, logical equivalence, tautology, contradiction, and normal forms.