Continuity and Galerkin Method

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Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Finite Elements: Problem with Limits

Covers the application of finite element methods to solve boundary value problems in one dimension.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Finite Difference Method: Approximating Derivatives and Equations

Introduces the finite difference method for approximating derivatives and solving differential equations in practical applications.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.