Lectures related to Finite Element Method: Construction and Integration

Finite Element Modeling: Systematization and Construction

Covers the systematization and construction of a 2D finite element model.

Finite Element Modeling: Systematization

Covers the systematization of 2D finite element modeling and treatment of curvilinear integrals.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Regular Curves: Parametrization and Tangent Vectors

Explores regular curves, examples like segments and functions, and curvilinear integrals along regular curves.

2D Finite Element Model: Systematization and Convergence

Covers the systematization and convergence of 2D finite element models.

Vector Fields Analysis

Explores vector fields analysis, covering curvilinear integrals, potential fields, and field connectivity conditions.

Curvilinear Integrals and Green's Theorem

Introduces curvilinear integrals, parameterization, and Green's Theorem for conservative fields.

Curvilinear Integrals

Covers the calculation of curvilinear integrals for a continuous function in R^n and the interpretation of the integral as the sum of small segments along a curve.

Curvilinear Integrals: Interpretation and Convexity

Explores the interpretation of curvilinear integrals in vector fields and the proof of potential fields.

Green's Theorem: Transforming Integrals in 2D

Covers Green's Theorem, transforming 2D integrals into 1D line integrals.

Surface Integrals: Parameterization and Regularity

Explains surface integrals, parameterization, and regularity of surfaces.

Curvilinear Integrals

Covers curvilinear integrals in R^n, focusing on continuous functions and curves.

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and domain potentials through practical examples and calculations.

Fields from Potential: Derivation and Curvilinear Integral

Explores deriving fields from a potential, curvilinear integrals, and necessary conditions for domains.

Total Differential: Definition and Integrals

Explores the definition of total differential and its applications in integral calculus.

Tangent and Normal Vectors: Curves in R^2

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

Curvilinear Integrals and Conservative Fields

Explores curvilinear integrals, conservative fields, and their implications in various contexts.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Magnetostatics: Magnetic Field and Force

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.