Transcript here

‫بسم هللا الرحمن الرحيم‬
Coupled Oscillations
Zain Yamani
Saudi Physical Society
Rabi-I, 1433
Agenda for Lecture-3:
1. Up-dates and administrative matters
2. Continue with matrices
3. Intro. Lagrangian Mechanics
Up-dates and
administrative matters
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!! 
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
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 we intend to do next Session!!