Courses

In 2021:

 

Linear Algebra and Applications

EXAM: click here for PDF (send email to alexei@impa.br or enter Google-meet using THIS LINK if you have questions)

March-June: Thursday at 10:30, Friday at 9:30. 

12/03 (video, notes), 18/03 (video, notes), 19/03 (video, notes), 25/03 (video, notes), 1/04 (video, notes), 08/04 (video, notes), 09/04 (video, notes), 

15/04 (video, notes), 16/04 (video, notes), 22/04 (video, notes), 23/04 (video, notes), 29/04 (video, notes), 30/04 (video, notes), 06/05 (video, notes),

07/05 (video, notes), 13/05 (video, notes), 14/05 (video, notes), 20/05 (video, notes), 21/05 (video, notes), 27/05 (video, notes),

28/05 (video1, video2, notes), 4/06 (video, notes), 10/06 (video, notes), 11/06 (video, notes), 17/06 (video, notes), 18/06 (video, notes)

  • List 1 for April 1. 
  • List 2 for April 22. 
  • List 3 for May 6. 
  • List 4 for May 20. 
  • List 5 for June 8.
  • List 6 for June 18. Please send to Julia (monitor) with a copy to me. 

EXAM: Friday, June 25 at 14:30.

Monitor: Julia Domingues, e-mail: juliahdomingues@hotmail.com 

Time for monitoria: please select HERE

Link for online class: it will be sent by email to all registered students, and you can ask me for this link by email.

Introduction to the Theory of Oscillations and Waves

January-February, Wednesday/Thursday/Friday, 10:00-12:00.

Online: feel free to ask me for the link by email.

  • Lecture notes: Part 1 [PDF in Portuguese], Part 2.2 [PDF in English], Part 3 [PDF in Portuguese, PDF in English]
  • Old videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 

Classes:

6/jan (video, notes), 7/jan (video, notes), 8/jan (video, notes), 13/jan (video, notes), 14/jan (video, notes), 15/jan (video, notes),

21/jan (video, notes),  22/jan (video, notes), 27/jan (video, notes), 28/jan (video, notes), 29/jan (video, notes),

3/fev (video, notes, YT1, YT2),  4/fev (video, notes), 5/fev (video, notes), 10/fev (video, notes),  11/fev (video, notes, YT1, YT2, YT3), 

12/fev (video, notes), 18/fev (video, notes), 19/fev (video, notes), 24/fev (video, notes, L1, L2, L3), 25/fev (video, notes), 26/fev (video)

Exercises:

  1. List 1 (PDF page 29) for 15/jan. 
  2. List 2 (PDF  pages 54-55) for 24/jan. Please send to me AND to the monitor.
  3. List 3 (see end of the notes) for 29/jan. Please send to me AND to the monitor.
  4. List 4 (see page  8 of the notes) for 5/feb. Please send to me AND to the monitor.
  5. List 5 (see last page of the notes) for 12/feb. Please send to me AND to the monitor.
  6. List 6 (see last pages of the notes) for 24/feb. Please send to me AND to the monitor.

Monitor: Ciro Campolina, e-mail: cs.campolina@gmail.com

In 2020:

Álgebra Linear e Aplicações March-June, Tue & Wed 15:30-17:00

Thermal and Statistical Aspects of Fluid Dynamics (together with Simon Thalabard) 

January-February, Tue, Wed, Fri 15:00-17:00, room 224 (starting on January 7)

Description

LECTURE NOTES: 

Section 1 (by Alexei Mailybaev)

  • Part 1 (classical mechanics)
  • Part 2 (basic statistical properties)
  • Part 3 (thermodynamic potentials)
  • Part 4 (Gibbs distribution and ideal gas)
  • Part 5 (phases and reactions)
  • Part 6 (ideal fluid dynamics)
  • Part 7 (thermal aspects of fluid flows)
  • Part 8 (multicomponent and multi-phase flows)
  • Questions   7/fev, 9:00, room 224

Section 2 (by Simon Thalabard)

In 2019:

August 1: Mini-course on Parametric Resonance 

At the São Paulo School of Advanced Sciences on NONLINEAR DYNAMICS

LECTURE NOTES

COURSE VIDEO

Temporary links: youtube1, youtube2, youtube3, youtube4

March-June: Fluid Dynamics

Tue, Wed 13:30-15:00, room 333

  1. Exercises (for Tue - April 2): see page 23 of Part1

Recommended literature: 

ACHESON, D. J. – Elementary Fluid Dynamics, Oxford University Press, 1990.
BATCHELOR, G. – An Introduction to Fluid Dynamics, Cambridge University Press, 1967.
CHORIN, A. J., MARSDEN, J. E. – A Mathematical Introduction to Fluid Mechanics, second edition, Springer-Verlag, 1990.
COURANT, R., FRIEDRICHS, K. O. – Supersonic Flow and Shock Waves, Springer-Verlag, 1976.
LANDAU L.D., LIFSHITZ, E.M. Fluid Mechanics. (Course of T.P., Vol.6).
WHITHAM, G. – Linear and Nonlinear Waves. New York, John Wiley, 1974.

January-February: Introduction to the Theory of Oscillations and Waves

  • Lecture notes: Part 1 [PDF in Portuguese], Part 2.2 [PDF in English], Part 3 [PDF in Portuguese, PDF in English]
  • Videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 
  1. Exercises (for Fri - 18/01),
  2. Exercises (for Wed - 30/01) - pages 54-55 in PDF of Part1.
  3. Exercises (for Wed - 6/02)
  4. Exercises (for Thu - 14/02)
  5. Exercises (for Fri - 22/02)

Some rather old notes

Exam questions with literature references 

Earlier:

Ordinary Differential Equations

Hydrodynamic Turbulence (reading course)

Spontaneous Stochasticity  (mini-course)

Bifurcations in ordinary differential equations

Fluid Dynamics

Introduction to the Theory of Oscillations and Waves

  • Lecture notes: Part 1 [PDF in Portuguese], Part 3 [PDF in Portuguese, PDF in English]
  • Videos on YouTube (in Portuguese): full collection at "Cursos do IMPA" 

Lectures on Boundaries of Stability Domains (mini-course)

Partial Differential Equations

Measure and Integration

Thermal Flow of Fluids

Stability and Catastrophes in Mechanical Systems

Introduction to the Lattice Boltzmann method for fluid dynamics (reading course)