Edx
date_range Débute le 23 avril 2019
event_note Se termine le 5 août 2019
list 10 séquences
assignment Niveau : Avancé
chat_bubble_outline Langue : Anglais
card_giftcard 420 points
Avis de la communauté
-
starstarstarstarstar

Les infos clés

credit_card Formation gratuite
verified_user Certification payante
timer 30 heures de cours

En résumé

The course is for engineering and physics majors.
You will learn how to build the solutions of important in physics differential equations and their asymptotic expansions.

The main topics include:
1.    Introduction to asymptotic series.
2.    Special functions.
3.    Saddle point techniques.
4.    Laplace method of solving differential equations with linear coefficients.
5.    Stokes phenomenon.

The course instructors are active researchers in a theoretical solid state physics.  Armed with the tools mastered while attending the course, the students will have solid command of the methods of tackling differential equations and integrals encountered in theoretical and applied  physics and material science.

You will learn:

  1. Basics of asymptotic expansions.
  2. Special functions.
  3. Saddle point techniques.
  4. Laplace method of solving differential equations with linear coefficients.
  5. Stokes phenomenon.

more_horiz Lire plus
more_horiz Lire moins
report_problem

Les prérequis

Good knowledge of real and basics of complex analysis, differential equations and general physics.

dns

Le programme

Week 1. Asymptotic series. Introduction 
  • Asymptotic series as approximation of definite integrals. 
  • Examples, optimal summation Taylor vs asymptotic expansions.
Week 2. Laplace-type integrals and stationary phase approximations
  • Zero term and full Laplace asymptotic series.
  • Asymptotics of Error and Fresnel integrals.
Week 3. Euler Gamma and Beta-functions, analytic continuation and asymptotics
  • Euler Gamma function: definition, functional equation and analytic continuation.
  • Hankel representation for Gamma-function. 
  • Beta and digamma functions.
  • Asymptotic expansions.
  • Application of Gamma functions for the computation of integrals.
Week 4. Saddle point approximation I 
  • Introduction to the method of saddle point approximation.
  • The search for optimal deformation of the contour.
  • Full asymptotic series.
  • Elementary applications of the saddle point approximation.
Week 5. Saddle point approximation II
  • Subtleties of a contour deformation.
  • Contribution of end points.
  • Higher order saddles.
  • Coalescent saddle and pole.
Week 6. Differential equations with linear coefficients. Laplace method I
  • Construction of the solution of the differential equations with linear coefficients in terms of Laplace type contour integrals.
  • Examples of solutions of second order differential equations
  • The general outline of the technique.
Week 7. Physical applications
  • 1D Coulomb potential  
  • Harmonic oscillator, method 1
  • Restricted harmonic oscillator 
  • Harmonic oscillator, method 2
Week 8. Stokes Phenomenon in asymptotic series and WKB approximation in Quantum Mechanics
  • Solution of Airy's equation by asymptotic series.
  • WKB approximation for solution of wave equations.
  • Asymptotics of Airy's function in the complex plane.
  • Stokes phenomenon.
Week 9. Differential equations with linear coefficients. Laplace method II (higher order equations)
  • Solutions of the differential equations of higher order by Laplace method.
  • More complicated examples.
  • Killer problems
 Week 10. Final Exam
record_voice_over

Les intervenants

Yaroslav Rodionov
Associate Professor
National University of Science and Technology MISIS

Konstantin Tikhonov
Researcher, Theoretical Physics
Landau Institute

assistant

La plateforme

EdX est une plateforme d'apprentissage en ligne (dite FLOT ou MOOC). Elle héberge et met gratuitement à disposition des cours en ligne de niveau universitaire à travers le monde entier. Elle mène également des recherches sur l'apprentissage en ligne et la façon dont les utilisateurs utilisent celle-ci. Elle est à but non lucratif et la plateforme utilise un logiciel open source.

EdX a été fondée par le Massachusetts Institute of Technology et par l'université Harvard en mai 2012. En 2014, environ 50 écoles, associations et organisations internationales offrent ou projettent d'offrir des cours sur EdX. En juillet 2014, elle avait plus de 2,5 millions d'utilisateurs suivant plus de 200 cours en ligne.

Les deux universités américaines qui financent la plateforme ont investi 60 millions USD dans son développement. La plateforme France Université Numérique utilise la technologie openedX, supportée par Google.

Vous êtes le concepteur de ce MOOC ?
Quelle note donnez-vous à cette ressource ?
Contenu
0/5
Plateforme
0/5
Animation
0/5