coupled oscillations zain yamani saudi physical society rabi-i, 1433 agenda for lecture-3:...
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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
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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
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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?!!
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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
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A good reference book: An Introduction to Linear Algebra with Applications, by Steven Roman
Intro. to Linear Algebra
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Intro. to Lagrangian Mechanics
What is Lagrangian Mechanics?
Why Lagrangian?
Example:
- projectile motion in 2-d
- simple harmonic oscillator
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What we intend to do next Session!!