Numerical Derivatives: Finite Difference Formulas

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Focuses on numerical modelling of atmospheric processes to predict weather and climate phenomena, covering key concepts and methods.

Covers the concept of numerical derivatives of order 1 and the importance of choosing a small fixed value for h.

Explores floating point numbers, LU decomposition, errors in numerical computations, and the impact of round-off errors.

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

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.

Discusses evaluation feedback, convergence, error analysis, and adaptive time steps in physics simulations.

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

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.