Lectures related to Numerical Integration: Order and Convergence

Root Finding Methods: Bisection and Secant Techniques

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

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.

Trade-offs in Data and Time

Explores trade-offs between data and time in computational problems, emphasizing diminishing returns and continuous trade-offs.

Numerical Integration

Covers the importance of reducing integration order for more efficient calculations.

Finite Differences and Finite Elements: Variational Formulation

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

Scientific Computing in Neuroscience

Explores scientific computing in neuroscience, emphasizing the simulation of neurons and networks using tools like NEURON, NEST, and BRIAN.

Mechanics of Slender Structure: Naturally Curly Hair in 3D

Delves into the mechanics of slender structures using naturally curly hair in 3D as an example.

Numerics: semester project

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

Computational Science and Engineering: Master Program Overview

Outlines the Master in Computational Science and Engineering program at EPFL, detailing its structure, projects, and career opportunities for graduates.

Numerical Analysis: Advanced Topics

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Monte Carlo Methods: Thermal Radiation Applications

Discusses the application of Monte Carlo methods in thermal radiation analysis, focusing on probability functions and numerical integration techniques.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Integration Techniques: Composite Quadrature Formulas

Covers numerical integration techniques, focusing on composite quadrature formulas and their applications for approximating integrals with improved accuracy.

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Numerical Methods: Stopping Criteria, SciPy, and Matplotlib

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

Stochastic Differential Equations: Mean-Field Inference

Explores inference for stochastic differential equations, focusing on numerical methods and convergence analysis.

Computational Geomechanics

Covers the basics of computational geomechanics, including poroelasticity, plasticity, and numerical methods for solving geotechnical problems.

Lagrange Interpolation: Numerical Integration Techniques

Covers Lagrange interpolation and its application in numerical integration techniques, focusing on both non-composite and composite methods of quadrature.

Numerical Methods: Bisection and Multidimensional Arrays

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