Descrição

Escola de Verão 2023

Professor: Alexei Mailybaev

Pré-requisitos: cursos de graduação em equações diferenciais ordinárias e álgebra linear.

Equações do movimento: princípio variacional, simetrias, leis de conservação. Oscilações: autovalores, estabilidade, ressonâncias. Ondas lineares: equações discretas e contínuas, o método espectral. Ondas não lineares: modelos matemáticos, soluções básicas, aplicações.

Referências:

• ARNOLD, V.I. – Lectures on Partial Differential Equations. Springer, 2004.

• ARNOLD, V.I. – Mathematical Methods of Classical Mechanics. Springer, 1989.

• LANDAU, L.D. and LIFSHITZ, E.M. – Mechanics. Pergamon Press, 1976.

• SEYRANIAN, A.M. and MAILYBAEV, A.A. – Multiparameter Stability Theory with Mechanical Applications. World Scientific, 2004.

• WHITHAM, G.B. – Linear and Nonlinear Waves. New York, Wiley, 1974.

IMPA - Instituto de Matemática Pura e Aplicada ©

https://www.impa.br | https://impa.br/videos 

Descrição

Professor: Alexei Mailybaev

Programa de Iniciação Científica 2013: Introdução à Teoria de Vibrações e Ondas

Pré-requisitos: cursos de graduação em equações diferenciais ordinárias e álgebra linear.

Equações do movimento: princípio variacional, simetrias, leis de conservação. Oscilações: autovalores, estabilidade, ressonâncias. Ondas lineares: equações discretas e contínuas, o método espectral. Ondas nonlineares: modelos matemáticos, soluções básicas, aplicações.

Referências:

• ARNOLD, V.I. - Mathematical Methods of Classical Mechanics. Springer, 1989.

• WHITHAM, G.B. - Linear and Nonlinear Waves. New York, Wiley, 1974.

https://www.impa.br | https://impa.br/videos

Instituto de Matemática Pura e Aplicada 

Complete playlist of Walter Lewin's 8.03 lecture videos, now hosted on For the Allure of Physics!

For the Allure of Physics

Course Description

Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string. In fact, without vibrations and waves, we could not recognize the universe around us at all!

The amazing thing is that we can describe many fascinating phenomena arising from very different physical systems with mathematics. This course will provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. You will learn that waves come from many interconnected (coupled) objects when they are vibrating together. We will discuss many of these phenomena, along with related topics, including mechanical vibrations and waves, sound waves, electromagnetic waves, optics, and gravitational waves.

Course Description

8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students in the process of problem solving.