1. 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 بسم الله الرحمن الرحيم

2. 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

3. 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?!!

4. 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

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

6. Intro. to Lagrangian Mechanics What is Lagrangian Mechanics? Why Lagrangian? Example: - projectile motion in 2-d - simple harmonic oscillator

7. What we intend to do next Session!!