Lectures related to Vectorization in Python: Efficient Computation with Numpy

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Discusses the bisection method for solving nonlinear equations and its implementation using Python with NumPy and Matplotlib.

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

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

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

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

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

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

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

Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.

Covers exercises related to numerical methods, focusing on computational algorithms and problem-solving strategies.

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

Covers the convergence of Newton's method and its applications in numerical analysis.

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.