Coupled OscillationsZain Yamani

Saudi Physical SocietyRabi-I, 1433

Agenda for Lecture-3:

1. Up-dates and administrative matters2. Continue with matrices3. Intro. Lagrangian Mechanics

الرحيم الرحمن الله بسم

Web-site: News/ hints/ scribbles

Interaction-2 will be posted

Some students needed to leave; others are

being requested to leave

Slight shuffle in TAing

Have your pens and papers ready!!

Up-dates and administrative matters

Intro. to Linear Algebra

- What is a matrix and why is it important?

• Solving algebraic equations with matrices

• Rotation by matrices

• Coupled Oscillations [T,V]!!!!!!!!

- Matrix algebra (adding, multiplying, commuting)

-Matrix determinant

-Square matrix inversion:

• Cofactors

• Row reduction

• a third way?? guess what?!!

Intro. to Linear Algebra

- Eigenvalues and eigenvectors of matrices

- Orthonormalization of eigenvectors

- The ordered basis set..

- Repeated eignenvalues (degeneracy)

- eigenvectors for symmetric matrices (of non-degenerate eigenvectors)

-Similarity of matrices

- Diagonalization of matrices

-Solving differential equations with matrices

A good reference book: An Introduction to Linear Algebra with Applications, by Steven Roman

Intro. to Linear Algebra

Intro. to Lagrangian Mechanics

What is Lagrangian Mechanics?

Why Lagrangian?

Example:

- projectile motion in 2-d

- simple harmonic oscillator

What we intend to do next Session!!