‫بسم هللا الرحمن الرحيم‬
Coupled Oscillations
Zain Yamani
Saudi Physical Society
Rabi-I, 1433
Agenda for Lecture-2:
1.
2.
3.
4.
Up-dates and administrative matters
Setting Sun turn red 
Intro. to Linear Algebra
Intro. Lagrangian Mechanics
Up-dates and
administrative matters
Groups formed
Web-site up-date (and modified its URL!!)
Interaction-1 posted
Please resubmit everything to your TA!!
About absences..
When you need to send a “chat” to me (alone)
Setting Sun turn red
Sum the sinusoids..
Fourier synthesis
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
- Eignenvalues 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