Modeling of Physical Phenomena

Basic information

Workload: 

60 hours

Prerequisite: 

Calculus in one real variable.

Syllabus: 

Dimensional analysis, Newtonian physics, conservation laws, basic examples (projectiles, harmonic movement). Introduction to Lagrange mechanics (simple and spherical pendulum, Kepler). Visualization of the phase portrait. Introduction to variational principles, from Euler-Lagrange to Pontryagin.

 

Teaching Plan

Bibliography

Mandatory: 

•    Fundamentals of Physics 1 - Mechanics - 9th Ed. 2012. Walker, Jearl;
•    Raymond A. Serway and John W. Jewett, Jr. Principles of Physics, Volume 1 - Classical Mechanics. Thomson Publisher, 2003;
•    Djairo Guedes de Figueiredo & Aloísio Freiria Neves. Applied Differential Equations. University Mathematical Collection-IMPA.
 

Complementary: 

•    Lopes, Arthur O. Introduction to Classical Mechanics - IMPA;
•    Lopes, Arthur O. Classical Mechanics Topics - IMPA;
•    Arnold, A. Weinstein and K. Vogtmann. Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60) Acadmic Press;
•    Arnold Sommerfeld, Mechanics. Lectures on Theoretical Physics Volume 1 - Academic Press;
•    Holm, D. Darryl, Dynamics and Symmetry - Imperial College Press