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Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433

بسم الله الرحمن الرحيم. Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433. Agenda for Lecture-2:. Up-dates and administrative matters Setting Sun turn red  Intro. to Linear Algebra Intro. Lagrangian Mechanics. Up-dates and administrative matters. Groups formed

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Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433

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  1. بسم الله الرحمن الرحيم Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433 Agenda for Lecture-2: Up-dates and administrative matters Setting Sun turn red  Intro. to Linear Algebra Intro. Lagrangian Mechanics

  2. 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)

  3. Setting Sun turn red

  4. Sum the sinusoids.. Fourier synthesis

  5. 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?!! 

  6. 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

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

  8. Intro. to Lagrangian Mechanics

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