Numerical Differentiation: Backward and Central Differences

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Explores numerical differentiation using finite differences and addresses the impact of errors in computer computations.

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

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

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

Covers error division and schemes for solving differential equations.

Explores numerical methods for fluid dynamics and techniques for handling fluid interfaces.

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Explores challenges in polynomial approximation, stability issues, and error analysis in numerical differentiation.