Calculus of Variations and Euler's Elastica

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Discusses numerical methods, focusing on stopping criteria, SciPy for optimization, and data visualization with Matplotlib.

Covers NumPy arrays and their graphical representations using Matplotlib, focusing on array creation, manipulation, and visualization techniques.

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.

Explores the Euler-Lagrange equation, convexity, and saddle point problems in variational calculus.

Introduces NumPy, focusing on array creation, manipulation, and its advantages for scientific computing.

Covers numerical methods for root finding, focusing on the secant and Newton's methods.

Explores unconfined flow in computational geomechanics, emphasizing weak form derivation and relative permeability.

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Covers ODE RK schemes, including explicit RK stages and accuracy computation.