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Introduction to Linear Algebra and Lagrangian Mechanics

Learn about the importance of matrices, solving algebraic equations, coupled oscillations, eigenvalues, eigenvectors, and Lagrangian mechanics. Reference book recommended. Get ready for the next session!

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Introduction to Linear Algebra and Lagrangian Mechanics

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  1. بسم الله الرحمن الرحيم Coupled Oscillations Zain Yamani Saudi Physical Society Rabi-I, 1433 Agenda for Lecture-3: Up-dates and administrative matters Continue with matrices Intro. Lagrangian Mechanics

  2. 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!! 

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

  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!!

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