Lectures related to Dynamic Systems in Biology

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Phase Portraits and Predator-Prey Models

Explores phase portraits in 2D systems and the dynamics of predator-prey models.

Numerical Methods: Iterative Techniques

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

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Non-linear Systems in 2D: Predator-Prey Models

Covers non-linear systems in 2D, focusing on predator-prey models and stability analysis of fixed points.

Nonlinear Equations: Problem Position

Introduces numerical methods for solving nonlinear equations, emphasizing the problem position and the Newton method for fixed points.

Numerical Methods: Fixed Point and Picard Method

Covers fixed point methods and the Picard method for solving nonlinear equations iteratively.

Fixed-Point Methods and Newton-Raphson

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.

Newton's Method: Fixed Point Iterative Approach

Covers Newton's method for finding zeros of functions through fixed point iteration and discusses convergence properties.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Nonlinear Equations: Fixed Point Method Convergence

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

Qualitative Analysis of Growth Models and Gene Regulation

Explores growth models for populations and gene regulation analysis.

Computational Geomechanics: Unconfined Flow

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

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Fixed Points and Stability

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.

Nonlinear Equations: Methods and Applications

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

Orientation Calculation in Geomatics

Explains how to calculate the orientation of a station in geomatics.

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.