Lectures related to Comparison of numerical-analysis software

Covers logical arrays, 3D surface plotting, parametric curves, interpolation, and fitting in Matlab.

Provides an overview of the Numerical Analysis course at EPFL, focusing on course organization, materials, and learning outcomes.

Introduction to Numerical Analysis

Introduces a course on numerical analysis, covering its importance, the MOOC, MATLAB, and Jupyter notebooks.

Floating Point Numbers: Representation and Errors

Introduces floating point number representation, round-off errors, and their impact on numerical computations.

Numerical Analysis: Algorithms and Concepts

Covers algorithms for mathematical problems, focusing on stability, precision, and critical result analysis.

Euler Retrograde Scheme

Explores the Euler retrograde scheme, its implicit nature, and application in solving differential equations.

Numerical Analysis: Jupyter Notebook Tutorial

Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.

Numerical Analysis of Differential Equations

Covers the numerical analysis of differential equations, focusing on methods and stability conditions.

Boundary Problems in 1D: Finite Differences

Covers chapter 10 on boundary problems in 1D using finite difference methods.

Runge-Kutta and Multi-Step Methods

Covers Runge-Kutta and multi-step methods in Chapter 6, including high-order methods and MATLAB examples.

Differential Equations: Approximation Methods and Analysis

Covers methods for approximating solutions to differential equations and their real-world applications.

Numerical Analysis: Interpolation and Approximation

Covers linear systems, non-linear equations, and interpolation for numerical analysis.

Numerical Analysis: Introduction to Interpolation Techniques

Covers the basics of numerical analysis, focusing on interpolation methods and their applications in engineering.

Jupyter Notebooks for Numerical Analysis

Covers the transition to Python and Jupyter notebooks for Numerical Analysis at EPFL, including interactive exercises and graded tests.

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

Systems of ODE

Explores stability and convergence in systems of ordinary differential equations.

Floating Point Numbers: Representation and Errors

Explores floating point numbers, their representation, precision, and associated errors.

Implicit Schemes in Numerical Analysis

Explores implicit schemes in numerical analysis, emphasizing stability and convergence properties in solving differential equations.

Structures and Mechanisms: Opening a Box

Explores the analysis of structures and mechanisms through a sample problem of opening a box with a string-held lid.

Convergence: Euler's Method

Explores stability and convergence in numerical methods for ODEs, focusing on Euler's progressive method.