Analyse numérique pour ingénieurs

Go to Course: https://www.coursera.org/learn/analyse-numerique

Introduction

**Course Review: Analyse numérique pour ingénieurs on Coursera** **Course Overview** "Analyse numérique pour ingénieurs" is a comprehensive online course offered on Coursera, structured as an introduction to numerical analysis for undergraduate students at the École Polytechnique Fédérale de Lausanne (EPFL). This course is intricately designed around the textbook "Introduction à l'analyse numérique" by J. Rappaz and M. Picasso, presenting foundational numerical tools and techniques utilized in engineering and applied mathematics. Covering the first seven chapters of the textbook, this course delves into interpolation, numerical differentiation and integration, the resolution of linear and nonlinear systems of equations, and numerical solutions to differential equations. **Course Syllabus Breakdown** The syllabus is well-structured and thoughtfully curated, facilitating a step-by-step understanding of numerical analysis. Here's a brief overview of the main topics covered: 1. **Interpolation**: - Learn about Lagrange interpolation and interval interpolation techniques, essential for approximating functions and understanding their behavior between known data points. 2. **Numerical Differentiation**: - This section prepares students to calculate derivatives using finite difference formulas, focusing on both first and second derivatives, a critical skill in various engineering applications. 3. **Numerical Integration**: - Students explore quadrature formulas including weights and points of integration, along with the precision of Gauss’ formulas, which are crucial for solving integrals numerically. 4. **Resolution of Linear Systems**: - Here, the course covers foundational methods like Gaussian elimination, LU decomposition, and LL^T decomposition, vital for solving linear systems typically encountered in engineering problems. 5. **Nonlinear Equations and Systems**: - This module introduces methods for tackling nonlinear equations and systems, including fixed-point methods and Newton's method, which are essential for real-world problem-solving. 6. **Differential Equations**: - Students study first-order differential equations, focusing on existence and uniqueness issues, along with Euler schemes and the resolution of first-order differential systems. 7. **Boundary Value Problems**: - The final chapter addresses one-dimensional boundary value problems using finite difference methods, covering both linear and nonlinear cases to round off the student's knowledge base. 8. **Final Exam**: - The course includes a final exam, accounting for 30% of the overall grade, ensuring that students have a practical mastery of the concepts learned. **Course Experience** The course employs a blend of theoretical concepts, practical applications, and problem-solving techniques, making it appealing for both theoretical enthusiasts and practitioners in the engineering field. Its interactive elements, such as quizzes and assignments, help reinforce learning and enhance understanding. The content is delivered with clarity, and real-world applications are emphasized throughout the modules, making the learning experience relevant and engaging. Given its strong academic foundation and hands-on approach, students can expect to build a solid grasp of numerical analysis, applicable in various engineering contexts. **Recommendation** I highly recommend "Analyse numérique pour ingénieurs" for anyone looking to deepen their understanding of numerical methods and their applications in engineering. Whether you are a current engineering student, a professional looking to upskill, or simply have an interest in numerical analysis, this course provides invaluable insights and knowledge. With the high-quality resources from EPFL and the structured approach of the syllabus, participants will emerge from the course with not just theoretical knowledge but practical skills that can be applied in real-world engineering tasks. Enroll in this course if you're ready to elevate your analytical capabilities and explore the fascinating world of numerical analysis!

Syllabus

Interpolation

Interpolation de Lagrange. Interpolation par intervalles.

Formules de différences finies pour approcher les dérivées premières et secondes.

Formules de quadrature. Poids et points d'intégration. Formules de Gauss.

Elimination de Gauss. Décomposition LU. Décomposition LL^T.

Equations non linéaires. Méthodes de point fixe. Méthode de Newton. Systèmes non linéaires.

Equations différentielles du premier ordre. Existence et unicité. Schémas d'Euler. Systèmes différentiels du premier ordre.

Un problème aux limites unidimensionnels linéaire. Méthode de différences finies. Un problème non linéaire.

Examen final (30% de la note)