Lectures related to Optimal Linear Response: Stochastic Dynamical Systems

Monetary Policy and Public Debt Analysis

Analyzes monetary and fiscal policy responses to public debt accumulation and the impact of Covid-19 on global economies.

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Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Numerical Analysis: Introduction to Computational Methods

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

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

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

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Kernel Regression: Basics and Applications

Explores kernel regression, the curse of dimensionality, and random features in neural networks.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

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

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Numerical Methods: Bisection and Multidimensional Arrays

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

Numerical Methods: Differential Equations

Covers the application of numerical methods to solve differential equations using MATLAB.

Numerical Analysis: Stability in ODEs

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

Advanced Analysis II: Cauchy Problem Resolution

Covers the numerical resolution of a Cauchy problem using separation of variables and discusses the conditions for the solution's validity.

Kernel Methods: Machine Learning

Covers Kernel Methods in Machine Learning, focusing on overfitting, model selection, cross-validation, regularization, kernel functions, and SVM.

Kernel Regression: K-nearest Neighbors

Covers the concept of kernel regression and K-nearest neighbors for making data linearly separable.

Numerical Methods for Boundary Value Problems

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