Analyse numérique pour ingénieurs from Coursera

Ce cours contient les 7 premiers chapitres d'un cours donné aux étudiants bachelor de l'EPFL. Il est basé sur le livre "Introduction à l'analyse numérique", J. Rappaz M. Picasso, Ed. PPUR. Des outils de base sont décrits dans les 5 premiers chapitres. Les deux derniers chapitres abordent la question de la résolution numérique d'équations différentielles. Plus précisement, nous allons étudier les chapitres suivants du livre :

Chapitre 1 : interpolation, comment approcher une fonction par un polynôme?

Chapitre 2 : comment approcher des dérivées par des formules de différences finies?

Chapitre 3 : comment approcher des intégrales par des formules de quadrature?

Chapitres 4,5,6 : comment résoudre des (grands) systèmes linéaires?

Chapitre 8 : comment résoudre des équations et systèmes d’équations nonlinéaires?

Chapitre 9 : comment approcher la solution d’une équations différentielle (problème à valeur initiale)?

Chapitre 10 : comment approcher la solution d’un problème aux limites unidimensionnel par une méthode de différences finies?

Un cours de deux heures est donc remplacé par des "video lectures" ainsi que les "quiz" correspondant. L'heure d'exercices est remplacée par un "exercice" où vous devrez faire des expériences numériques avec un programme matlab ou octave, et démontrer des résultats théoriques "peer review". Un questionnaire a choix multiple aura lieu à la fin du cours (30% de la note).

Il faut obtenir 60% de la note pour avoir le “Course Certificate”.

Pour les étudiants EPFL, les heures de cours selon l'horaire is-academia sont maintenues. Vous devez visionner les "video lectures" de la semaine et faire les "quiz" avant l'heure de cours. Lors de la première heure de cours, je résoudrai l'exercice théorique (cet exercice theorique sera proposé comme "peer review" pour les étudiants externes). Une question du même type pourrait être posée lors de l'examen de juin. Lors de la deuxième heure de cours, je répondrai aux questions et je vous aiderai à faire l'"exercice" si nécessaire.

Le temps de travail estimé est le suivant. Il faut compter deux heures pour visualiser les "video lectures" et répondre aux "quiz". Il faut compter une heure pour faire l'"exercice", qui demande de compléter un programme matlab (ou octave) et une heure pour faire l'exercice théorique "peer review" soit cinq heures en tout. Après ces cinq heures, vous devriez avoir acquis la matière.

What's inside

Syllabus

Interpolation

Interpolation de Lagrange. Interpolation par intervalles.

Dérivation numérique

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

Intégration numérique

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

Résolution de systèmes linéaires

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

Equations et systèmes d'équations non linéaires

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

Equations et systèmes d'équations différentielles

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

Problèmes aux limites unidimensionnels.

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

Examen final

Examen final (30% de la note)

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Enseigne des méthodes numériques fondamentales utilisées en ingénierie et en sciences

Bien adapté aux étudiants de premier cycle en ingénierie, mathématiques et sciences

Couvre des sujets essentiels de l'analyse numérique, notamment l'interpolation, l'intégration et la résolution d'équations différentielles

Comprend des exercices et des quiz pour renforcer la compréhension

Dispose d'examens finaux pour évaluer l'apprentissage

Nécessite des connaissances préalables en mathématiques, notamment en calcul et en algèbre linéaire

Reviews summary

Lucid numerical analysis for engineers

This course covers the basics of numerical analysis in a clear and concise manner. It is well-suited for engineering students who need a strong foundation in this area. The course is well-structured and the materials are easy to follow. The professor is knowledgeable and engaging.

Course outline and materials are organized well.

Explanations are lucid and easy to follow.

"Clair et concis"

Covers all the basics of numerical analysis.

Knowledgeable and interesting to listen to.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Analyse numérique pour ingénieurs with these activities:

Review interpolation, differentiation, and integration

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Reinforce your knowledge of basic numerical analysis concepts before starting the course.

Browse courses on Interpolation

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Review lecture notes or textbooks on interpolation, differentiation, and integration.
Solve practice problems related to these concepts.

Review different types of interpolation methods

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Review the different types of interpolation methods to strengthen your understanding of the concepts covered in the course.

Browse courses on Interpolation

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Read about Lagrange interpolation and interval interpolation.
Practice applying these methods to numerical examples.
Compare the advantages and disadvantages of each method.

Follow tutorials on solving systems of linear equations

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Following tutorials on solving systems of linear equations will provide additional guidance and practice beyond the course materials.

Browse courses on Linear Systems

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Find tutorials on different methods for solving systems of linear equations.
Follow the tutorials step-by-step to solve practice problems.
Compare the different methods and identify their strengths and weaknesses.

Eight other activities

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Solve practice problems on numerical differentiation

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Solving practice problems will reinforce the concepts and techniques of numerical differentiation covered in the course.

Browse courses on Numerical Differentiation

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Find practice problems on numerical differentiation.
Apply the finite difference formulas to approximate derivatives.
Analyze the accuracy and error of your approximations.

Follow tutorials on solving linear systems

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Enhance your understanding of solving linear systems by following guided tutorials.

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Find tutorials on solving linear systems using different methods (e.g., Gauss elimination, LU decomposition).
Work through the tutorials, implementing the methods in a programming language.
Test your understanding by solving linear systems of varying sizes.

Participate in peer review sessions for solving differential equations

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Peer review sessions will provide opportunities to discuss different approaches to solving differential equations and receive feedback on your solutions.

Browse courses on Differential Equations

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Find a study group or join an online forum for peer review.
Present your solutions to differential equations problems.
Provide constructive criticism and feedback to your peers.
Incorporate feedback into your own understanding and problem-solving approach.

Create a presentation on numerical integration

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Creating a presentation on numerical integration will deepen your understanding of the concepts and enable you to effectively communicate them.

Browse courses on Numerical Integration

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Research different numerical integration methods.
Develop a presentation outline covering the key concepts.
Create visual aids and examples to illustrate the methods.
Practice presenting your findings.

Participate in peer review of theoretical exercises

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Deepen your understanding of theoretical concepts by engaging in peer review of exercises.

Browse courses on Numerical Analysis

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Join a peer review group or find a study partner.
Work on theoretical exercises assigned in the course.
Share your solutions with your group and provide feedback on others' solutions.
Discuss different approaches, identify errors, and collectively improve understanding.

Develop a MATLAB or Octave program for solving nonlinear equations

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Developing a program for solving nonlinear equations will provide hands-on experience and deepen your understanding of the numerical methods involved.

Browse courses on Nonlinear Equations

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Review the concepts of fixed-point iteration and Newton's method.
Design and implement a MATLAB or Octave program to solve nonlinear equations.
Test your program on various nonlinear equations.
Analyze the convergence and accuracy of your program.

Practice solving nonlinear equations and systems

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Sharpen your skills in solving nonlinear equations and systems through repetitive practice.

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Find online resources or textbooks with collections of nonlinear equations and systems.
Solve the problems using different methods (e.g., fixed point iteration, Newton's method).
Analyze your solutions and identify the convergence behavior of the methods.
Compare your results with known solutions or use error analysis to assess accuracy.

Develop a summary of numerical methods for solving differential equations

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Enhance your understanding and retention of numerical methods for differential equations by creating a comprehensive summary.

Browse courses on Numerical Analysis

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Review lecture notes, textbooks, and online resources on numerical methods for differential equations.
Identify the key concepts, methods, and algorithms used in solving differential equations numerically.
Organize and write a summary that clearly explains the different methods, their advantages, and limitations.
Include examples and illustrations to enhance understanding.

Career center

Learners who complete Analyse numérique pour ingénieurs will develop knowledge and skills that may be useful to these careers:

Numerical Analyst

Numerical Analysts develop mathematical models and computational methods to solve complex problems in science, engineering, and finance. They use their knowledge of numerical methods, such as interpolation, numerical integration, and linear algebra, to develop algorithms that can be implemented on computers. The course, Analyse numérique pour ingénieurs, provides a strong foundation in these numerical methods, which would be valuable for anyone pursuing a career as a Numerical Analyst.

See salaries and explore the career path for Numerical Analyst

Data Analyst

Data Analysts use data to solve business problems. They collect, clean, and analyze data to identify trends and patterns. To be successful, Data Analysts need to have a strong understanding of numerical methods, such as those taught in Analyse numérique pour ingénieurs. This course can help Data Analysts develop the skills they need to effectively analyze data and communicate their findings to stakeholders.

See salaries and explore the career path for Data Analyst

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They use their knowledge of numerical methods to develop algorithms that can be used to predict future financial trends. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts use mathematical models to solve problems in business and industry. They use their knowledge of numerical methods to develop algorithms that can be used to optimize operations and improve efficiency. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Operations Research Analyst

Financial Analyst

Financial Analysts use numerical methods to analyze financial data and make investment recommendations. They use their knowledge of mathematics, statistics, and economics to develop models that can predict future financial trends. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Financial Analyst

Software Engineer

Software Engineers design, develop, and maintain software applications. They use their knowledge of numerical methods to develop algorithms that can be used to solve complex problems. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Software Engineer

Research Scientist

Research Scientists conduct research in a variety of fields, including science, engineering, and medicine. They use their knowledge of numerical methods to develop models that can be used to simulate physical phenomena and analyze data. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Research Scientist

Computational Scientist

Computational Scientists use computers to solve complex problems in science and engineering. They use their knowledge of numerical methods to develop algorithms that can be used to simulate physical phenomena and analyze data. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Computational Scientist

Machine Learning Engineer

Machine Learning Engineers design, develop, and maintain machine learning models. They use their knowledge of numerical methods to develop algorithms that can be used to train and evaluate machine learning models. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Machine Learning Engineer

Data Scientist

Data Scientists use data to solve problems in business, industry, and government. They use their knowledge of numerical methods to develop algorithms that can be used to analyze data and extract insights. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Data Scientist

Actuary

Actuaries use mathematics and statistics to assess risk and uncertainty. They use their knowledge of numerical methods to develop models that can be used to predict future events. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Actuary

Systems Analyst

Systems Analysts design, develop, and maintain computer systems. They use their knowledge of numerical methods to develop algorithms that can be used to optimize system performance. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Systems Analyst

Risk Analyst

Risk Analysts use mathematical and statistical models to assess risk and uncertainty. They use their knowledge of numerical methods to develop models that can be used to predict future events. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Risk Analyst

Insurance Analyst

Insurance Analysts use mathematical and statistical models to assess risk and uncertainty. They use their knowledge of numerical methods to develop models that can be used to predict future events. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Insurance Analyst

Financial Engineer

Financial Engineers use mathematical and statistical models to analyze financial data and develop investment strategies. They use their knowledge of numerical methods to develop algorithms that can be used to predict future financial trends. The course, Analyse numérique pour ingénieurs, provides a strong foundation in the numerical methods that are essential for success in this field.

See salaries and explore the career path for Financial Engineer