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Prof. François Golse
and
Prof. Yvan Martel
Une fonction discontinue peut-elle être solution d'une équation différentielle? Comment définir rigoureusement la masse de Dirac (une "fonction" d'intégrale un, nulle partout sauf en un point) et ses dérivées? Peut-on définir une notion de "dérivée d'ordre fractionnaire"? Cette initiation aux distributions répond à ces questions - et à bien d'autres.
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What's inside
Syllabus
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Syllabus
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Cours 4
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Cours 6
Cours 7
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Une initiation aux distributions pour comprendre les fonctions discontinues, la masse de Dirac et les dérivées d'ordre fractionnaire
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Adequate initiation to distribution theory
Based on the reviews provided, learners seem to have a positive experience with this course. Students appear to be interested in what the course covers. Overall, reviews are positive but do not showcase enough information to be confident in our summary.
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 Initiation à la théorie des distributions with these
activities:
Find a mentor who can help you with distributions
Show steps
Finding a mentor can help you to learn more about distributions and to develop your skills. A mentor can provide you with guidance and support.
Show steps
-
Talk to your instructor about finding a mentor.
-
Network with other students and professionals.
-
Attend conferences and workshops.
Review basic calculus concepts
Show steps
This course is heavily reliant on calculus, so it will be helpful to review some of the basics, such as limits, derivatives, and integrals.
Browse courses on
Calculus
Show steps
-
Read over your calculus notes or textbook.
-
Do some practice problems.
-
Take a practice quiz or exam.
Follow online tutorials on distributions
Show steps
There are many helpful online tutorials that can provide a more in-depth explanation of distributions. Watching these tutorials can help you to better understand the concepts covered in class.
Browse courses on
Distributions
Show steps
-
Search for online tutorials on distributions.
-
Watch a few of the tutorials.
-
Take notes on the key concepts.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve practice problems on distributions
Show steps
Solving practice problems is a great way to test your understanding of distributions. There are many practice problems available online and in textbooks.
Browse courses on
Distributions
Show steps
-
Find some practice problems on distributions.
-
Solve the problems.
-
Check your answers.
Join a study group
Show steps
Studying with other students can help you to learn the material more effectively. You can discuss the concepts with each other, work on problems together, and quiz each other.
Show steps
-
Find a study group to join.
-
Attend the study group meetings.
-
Participate in the discussions.
Create a presentation on distributions
Show steps
Creating a presentation on distributions can help you to organize your thoughts and deepen your understanding of the material. You can present your presentation to your classmates or to your instructor.
Browse courses on
Distributions
Show steps
-
Choose a topic for your presentation.
-
Research your topic.
-
Create your presentation.
-
Practice your presentation.
-
Give your presentation.
Participate in a math competition
Show steps
Participating in a math competition can help you to push yourself and to learn new things. There are many different math competitions available, so you can find one that is appropriate for your skill level.
Browse courses on
Distributions
Show steps
-
Find a math competition to participate in.
-
Study for the competition.
-
Compete in the competition.
Volunteer as a math tutor
Show steps
Volunteering as a math tutor can help you to solidify your understanding of distributions while also helping others to learn. You can volunteer at a local school or tutoring center.
Show steps
-
Find a place to volunteer.
-
Create lesson plans for your students
-
Prepare for and lead sessions
Find a mentor who can help you with distributions
Show steps
Finding a mentor can help you to learn more about distributions and to develop your skills. A mentor can provide you with guidance and support.
Show steps
Show steps
Show steps
- Talk to your instructor about finding a mentor.
- Network with other students and professionals.
- Attend conferences and workshops.
Review basic calculus concepts
Show steps
This course is heavily reliant on calculus, so it will be helpful to review some of the basics, such as limits, derivatives, and integrals.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- Read over your calculus notes or textbook.
- Do some practice problems.
- Take a practice quiz or exam.
Follow online tutorials on distributions
Show steps
There are many helpful online tutorials that can provide a more in-depth explanation of distributions. Watching these tutorials can help you to better understand the concepts covered in class.
Browse courses on
Distributions
Show steps
Show steps
Show steps
- Search for online tutorials on distributions.
- Watch a few of the tutorials.
- Take notes on the key concepts.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Solve practice problems on distributions
Show steps
Solving practice problems is a great way to test your understanding of distributions. There are many practice problems available online and in textbooks.
Browse courses on
Distributions
Show steps
Show steps
Show steps
- Find some practice problems on distributions.
- Solve the problems.
- Check your answers.
Join a study group
Show steps
Studying with other students can help you to learn the material more effectively. You can discuss the concepts with each other, work on problems together, and quiz each other.
Show steps
Show steps
Show steps
- Find a study group to join.
- Attend the study group meetings.
- Participate in the discussions.
Create a presentation on distributions
Show steps
Creating a presentation on distributions can help you to organize your thoughts and deepen your understanding of the material. You can present your presentation to your classmates or to your instructor.
Browse courses on
Distributions
Show steps
Show steps
Show steps
- Choose a topic for your presentation.
- Research your topic.
- Create your presentation.
- Practice your presentation.
- Give your presentation.
Participate in a math competition
Show steps
Participating in a math competition can help you to push yourself and to learn new things. There are many different math competitions available, so you can find one that is appropriate for your skill level.
Browse courses on
Distributions
Show steps
Show steps
Show steps
- Find a math competition to participate in.
- Study for the competition.
- Compete in the competition.
Volunteer as a math tutor
Show steps
Volunteering as a math tutor can help you to solidify your understanding of distributions while also helping others to learn. You can volunteer at a local school or tutoring center.
Show steps
Show steps
Show steps
- Find a place to volunteer.
- Create lesson plans for your students
- Prepare for and lead sessions
Career center
Learners who complete Initiation à la théorie des distributions will develop knowledge and skills
that may be useful to these careers:
Theoretical Physicist
Theoretical Physicist
Theoretical Physicists use mathematics to derive models that describe the physical universe. While Theoretical Physicists may use a variety of mathematical tools, an “Initiation à la théorie des distributions” will prove helpful to anyone interested in quantum field theory, cosmology, or particle physics. The study of distributions is a key mathematical technique used in these fields to describe physical phenomena.
Mathematician
Mathematician
Mathematicians use mathematical techniques to solve problems and develop new theories. While many Mathematicians work in pure mathematics, others use these techniques to solve practical problems in fields such as finance, engineering, and data science. An “Initiation à la théorie des distributions” will prove useful to any Mathematician interested in functional analysis, differential equations, or mathematical physics.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to solve problems in the financial industry. An “Initiation à la théorie des distributions” will provide a strong foundation in the mathematical techniques used by Quantitative Analysts, particularly those working in risk management or derivatives pricing.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical techniques to solve problems in a variety of industries, from manufacturing to healthcare. An “Initiation à la théorie des distributions” will prove useful to Operations Research Analysts interested in using advanced mathematical techniques to solve real-world problems.
Physicist
Physicist
Physicists use the fundamental principles of physics to explain the behavior of matter and energy. While Physicists may work in a range of fields, from astrophysics to nuclear physics, an “Initiation à la théorie des distributions” will be a valuable addition to the repertoire of skills for any Physicist working in theoretical physics.
Financial Risk Manager
Financial Risk Manager
Financial Risk Managers use mathematical and statistical techniques to assess and manage financial risk. An “Initiation à la théorie des distributions” will prove useful to Financial Risk Managers interested in using advanced mathematical techniques to analyze and manage financial risk.
Economist
Economist
Economists use mathematical and statistical techniques to analyze economic data and make predictions about the future. An “Initiation à la théorie des distributions” will prove useful to Economists interested in using advanced mathematical techniques to analyze economic data.
Scientific Researcher
Scientific Researcher
Scientific Researchers may study a wide range of topics, from the development of new medical treatments to the exploration of our solar system. An “Initiation à la théorie des distributions” will be a valuable addition to the repertoire of skills for any Scientific Researcher working in theoretical mathematics or theoretical physics.
Statistician
Statistician
Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. While Statisticians may work in a variety of fields, from healthcare to finance, an “Initiation à la théorie des distributions” will prove useful to anyone interested in using advanced mathematical techniques to analyze data.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. While Software Engineers may work in a variety of industries, from healthcare to finance, an “Initiation à la théorie des distributions” will prove useful to anyone interested in using mathematical techniques to solve problems in software development.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. An “Initiation à la théorie des distributions” will prove useful to Financial Analysts interested in using advanced mathematical techniques to analyze financial data.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. An “Initiation à la théorie des distributions” will prove useful to Actuaries interested in using advanced mathematical techniques to analyze risk and uncertainty.
Computer Scientist
Computer Scientist
Computer Scientists use mathematical and computational techniques to solve problems in a variety of fields, from artificial intelligence to computer graphics. An “Initiation à la théorie des distributions” will prove useful to Computer Scientists interested in using advanced mathematical techniques to solve problems in computer science.
Data Analyst
Data Analyst
Data Analysts use mathematical and statistical techniques to analyze data and make recommendations. While Data Analysts may work in a variety of industries, from healthcare to finance, an “Initiation à la théorie des distributions” will prove useful to anyone interested in using advanced mathematical techniques to analyze data.
Data Scientist
Data Scientist
Data Scientists use mathematical and statistical techniques to extract insights from data. While Data Scientists may work in a variety of industries, from healthcare to finance, an “Initiation à la théorie des distributions” will prove useful to anyone interested in using advanced mathematical techniques to solve real-world problems.
For more career information including salaries, visit:
OpenCourser.com/course/qfnkqs/initiation
Reading list
We've selected 17 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Initiation à la théorie des distributions.
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Ce livre classique en deux volumes est une introduction complète à la théorie des distributions, écrite par un pionnier dans le domaine. Il aborde les aspects mathématiques fondamentaux ainsi que les applications en physique.
Cet ouvrage en cinq volumes est une référence complète sur la théorie des distributions. Il couvre un large éventail de sujets, des fondements mathématiques aux applications en physique, en analyse et en ingénierie.
Ce livre offre une introduction rigoureuse et complète à la théorie des distributions. Il couvre les aspects théoriques fondamentaux ainsi que les applications en théorie des équations aux dérivées partielles et en physique.
Traite de manière approfondie les distributions, les équations aux dérivées partielles et les espaces de Sobolev, apportant un éclairage complémentaire sur les concepts abordés dans le cours.
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Couvre les sujets avancés en analyse, y compris la théorie des distributions, les espaces de Sobolev et les équations aux dérivées partielles, offrant une perspective plus large sur le sujet.
Ce livre fournit une introduction accessible à la théorie des distributions dans le contexte des équations aux dérivées partielles. Il aborde les applications en physique, en ingénierie et en mathématiques.
Fournit une approche moderne de la théorie des distributions, couvrant des sujets avancés tels que les opérateurs pseudo-différentiels.
Fournit une référence approfondie sur la transformée de Fourier, comprenant des applications dans divers domaines scientifiques et techniques.
Explore les applications des distributions dans les équations aux dérivées partielles, fournissant des exemples concrets et des techniques de résolution.
Ce livre fournit une introduction accessible à la théorie des distributions et à ses applications en analyse fonctionnelle et en équations aux dérivées partielles.
Fournit une introduction complète aux espaces de Sobolev, un sujet étroitement lié à la théorie des distributions, avec des applications en analyse et en physique.
Lie la théorie des distributions aux équations aux dérivées partielles, fournissant des outils pour résoudre des problèmes complexes dans des domaines tels que la physique et l'ingénierie.
Ouvrage fondateur sur la théorie des distributions, il présente les concepts fondamentaux et fournit des exemples concrets pour illustrer leur utilisation.
Save
Présente une approche non traditionnelle de la théorie des distributions, mettant l'accent sur les applications dans des domaines tels que la physique et l'ingénierie.
Fournit une introduction concise à la théorie des distributions et à la transformée de Fourier, mettant en évidence leur importance dans l'analyse harmonique.
Offre une introduction rigoureuse à la théorie des distributions, adaptée aux étudiants de deuxième cycle ou de recherche.
Offre une introduction accessible à la théorie des distributions, adaptée aux étudiants de premier cycle ou de début de cycle supérieur.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/qfnkqs/initiation
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Via
Coursera
Institution
École Polytechnique
Instructors
Prof. François Golse
Prof. Yvan Martel
Language
Français
Good to know
Une initiation aux distributions pour comprendre les fonctions discontinues, la masse de Dirac et les dérivées d'ordre fractionnaire
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