Transcript here

‫بسم هللا الرحمن الرحيم‬
Coupled Oscillations
Zain Yamani
Saudi Physical Society
Rabi-I, 1433
Agenda for Lecture-4:
1. What’s special today?
2. Conclude Linear Algebra
3. Intro. Lagrangian Mechanics
What’s special today?
Mid-way through the course!
You will come into action 
I will work a bit on the interactions at the end
of the Session, in sha’a Allah.
Please make sure you are in touch with
your TA!! 
Continue with 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
Intro. to Linear Algebra
A good reference book: An Introduction to Linear
Algebra with Applications, by Steven Roman
Intro. to Lagrangian Mechanics
What is Lagrangian Mechanics?
Why Lagrangian?
Example:
- projectile motion in 2-d
- simple harmonic oscillator
What do we intend to do next Session?!!