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REVIEW: Separation of Variables

REVIEW: Separation of Variables. Fourier’s Theorem. Friday Sept 17th: Linear Algebra. Vector/matrix operations Index notation Determinants Cartesian position vectors Eigenvalues /eigenvectors. Scalars and vectors. A scalar a is just a single number.

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REVIEW: Separation of Variables

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  1. REVIEW:Separation of Variables

  2. Fourier’s Theorem

  3. Friday Sept 17th: Linear Algebra Vector/matrix operations Index notation Determinants Cartesian position vectors Eigenvalues/eigenvectors

  4. Scalars and vectors • A scalara is just a single number. • A vector is, in the simplest definition, just a list of numbers:

  5. Matrices

  6. Determinant of a matrix

  7. Determinant of a matrix

  8. Determinant of a matrix

  9. Determinant of a matrix

  10. Matrix-vector multiplication, linear systems

  11. Cross product

  12. A linear system beach 60% speldfar, 40% schwartz ? ocean

  13. A linear system Crimea R. 90% speldfar, 10% schwartz C beach 60% speldfar, 40% schwartz ocean R Rollinonthe R. 40% speldfar, 60% schwartz

  14. Beach sand is 40% from Crimea R., 60% from Rollinonthe R.

  15. Cartesian position vectors unit vectors

  16. Cartesian position vectors Right-handed unit vectors Left-handed

  17. Matrices as transformations

  18. Matrices as transformations

  19. Matrices as transformations reversible

  20. Matrices as transformations reversible

  21. Matrices as transformations

  22. Matrices as transformations

  23. Matrices as transformations

  24. Matrices as transformations

  25. Eigenvalues and eigenvectors Typo on p. 50

  26. Eigenvalues and eigenvectors (special matrix)

  27. Eigenvalues and eigenvectors

  28. Finding eigvals and eigvecs

  29. Example: eigvals 3rd order polynomial equation

  30. Example: eigvecs =

  31. Example: eigvecs =

  32. Homework Section 4.1, Section 4.2, Section 4.3, omit #1, Section 4.4, plus:

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